By John Banzhaf. The author's own reference page identifies the article as Rutgers Law Review, volume 19, starting p. 317, 1965. That bibliographic evidence does not imply that the article's complete text was inspected.
By Lloyd Shapley. RAND's original report record identifies the year 1952 and document P-295; the later book chapter is a distinct publication record.
The abstract identifies the axiomatic construction of a value. The four-axiom decomposition and uniqueness proof in Shapley value axioms are stated explicitly here.
Primary publication: Mathematics of Operations Research 19(2), pp. 257–266. Publisher record.
Relevant locators: §1, printed p. 258, definition using signed integer edge weights and the nonnegative-weight convex case; §2.2, printed p. 260, discussion preceding Lemma 4. The self-loop extension and the elementary representation and convexity arguments are stated and proved directly in the solutions.
Original publication: Contributions to the Theory of Games II, pp. 193–216. Publisher record: doi.org/10.1515/9781400881970-012
Publisher record for the reprint in Classics in Game Theory, pp. 46–68: www.degruyterbrill.com/document/doi/10.1515/9781400829156-011/html
The paper develops extensive-form games and Kuhn's theorem relating mixed strategies, behavioural strategies and perfect recall. The finite two-round construction is proved directly in the examination solution.
The section “The Expected Utility Property” states the finite-lottery expected utility formula and connects it to the preceding preference axioms. The source's title misspells the second surname; the conventional name used here is Oskar Morgenstern.
The final paragraph states Tutte's theorem on perfect matchings in terms of the number of components of odd integer order after deleting a vertex subset. The worked perfect matching theorem for a cubic graph with at most two bridges uses this criterion directly.
Published in Journal of Statistical Mechanics: Theory and Experiment, P10008. Author preprint: arxiv.org/abs/0803.0476
Relevant passages: §1, Equation (1), network modularity; §2, Method, pp. 4–5 of the preprint, local optimization and aggregation.
Relevant passages: Network formalism, mean local clustering coefficient; New measures of small-world-ness, Definitions 1–2 and relative clustering/path-length ratio.
SIAM Journal on Computing 5(2), June 1976, pp. 266–283; DOI 10.1137/0205021. R. Endre Tarjan is Robert Endre Tarjan.
Cited passages: Abstract; Information & Authors: volume 5, issue 2, June 1976.
Oak Ridge National Laboratory technical report ORNL/TM-12203, November 1992.
Cited passages: §2.2, Lemma 1 and Theorem 2.2; §3.1–3.2, Theorems 3.1–3.3.
Publisher: Springer (book); University of Hamburg author site (preview host).
Cited passages: Diestel, Graph Theory, Chapter 2, Exercise 23; Diestel, Graph Theory, Section 2.1, Theorem 2.1.1 and its lower-bound argument; Diestel, Graph Theory, fourth electronic edition, Section 2.1, definition of vertex cover.
Published in Springer, Graduate Texts in Mathematics 173.
The linked University of Edinburgh mirror is the third electronic edition, 2005. Supporting locators here refer to printed pp. 165–167 of that edition, rather than to differently paginated author-hosted previews or later editions.
Third electronic edition (2005), §1.5, Trees and forests, pp.13–15: unique paths in trees, rooted-tree order and leaves.
Cited passages: Section 1.7, printed page 20 and Figure 1.7.3: contracting an edge to one vertex; Section 1.7, printed pages 18–21: subdivisions and Proposition 1.7.3(i); Section 1.7, printed pages 19–20, Corollary 1.7.2: finite minors by deletions and contractions.
Cited passages: Diestel, Graph Theory, Section 1.1; Diestel, Graph Theory, Section 1.5.
Cited passages: Section 4.4, printed page 111, Theorem 4.4.6, equivalence of planarity and exclusion of K5 and K3,3 minors.
Chapter preview from Graph Theory by Reinhard Diestel.
Published in Graph Theory.
Publisher: Springer (book); University of Hamburg author site (preview host).
Cited passages: Diestel, Graph Theory, Chapter 10, opening paragraph, printed p. 323: Hamilton cycles, Hamilton paths, and the contrast with Euler tours; Diestel, Graph Theory, §10.1, Theorem 10.1.1, printed p. 324; Diestel, Graph Theory, §10.1, printed pp. 323–324: necessary minimum degree two and 2-connectivity.
Chapter 6 of Graph Theory by Reinhard Diestel, by Reinhard Diestel. Springer publishes the book; the author’s University of Hamburg site hosts the preview. No edition, publication year or revision date is established from this preview.
Cited passages: Chapter 6 opening, printed p. 155 (PDF p. 1): signed amounts and nonterminal conservation.; §6.2, printed p. 158 (PDF p. 4): independently specified orientation capacities, conditions F1/F2′/F3 and source/sink cut definition.; §6.2, printed p. 159 (PDF p. 5): Proposition 6.2.1, cancellation proof, total-value definition, footnote 4 on negative values, capacity upper bound and Theorem 6.2.2..
Publisher: arXiv (repository).
Cited passages: Section 1, Introduction, opening two paragraphs: deletion/contraction definition and minor-model conditions (i)–(iii).
Publisher: MIT OpenCourseWare.
Cited passages: Polyanskiy and Wu, MIT 6.441 course notes, Section 5.3, Theorem 5.3.
Cited passages: Chapter 1, Definition 1.3, printed p. 8; Theorem 1.1(4), printed p. 10.
Cited passages: Section 2.4, Definition 2.4 and Theorem 2.5(1), printed pp. 26–27; Theorem 2.1, printed p. 20; Theorem 2.3(1,3), printed p. 23; Theorem 2.4(2) and Corollary 2.4, printed p. 24; Theorem 2.4(1) and its proof, printed p. 24: I(X;X) is infinite for a non-discrete distribution; Theorem 2.4(3), printed p. 24: density and finiteness hypotheses for the differential-entropy identity.
Cited passages: MIT 6.441, Chapter 2, Definition 2.4 and Theorem 2.5(1); MIT 6.441, Chapter 2, note following Theorem 2.5.
Cited passages: §23.2, Definition 23.1 and Theorem 23.2, printed pp. 242–243: reconstruction alphabets, separable distortion and the information converse.
Cited passages: §24.1, Theorem 24.1, printed pp. 246–247; §24.2, Theorem 24.2, printed p. 247: memoryless source hypotheses, single-letterization and asymptotic achievability.
Cited passages: §25.1.1, Bernoulli Source, printed p. 255: binary Hamming distortion, achievable backward test channel and converse.
Published in The Bell System Technical Journal, volume 27, pp. 379–423 and 623–656.
Cited passages: Section 20, properties 8–9, reprint pp. 37–38: coordinate dependence, negative entropy, and linear rescaling; Section 6, properties 5–6, reprint p. 12; title page identifies C. E. Shannon and the 1948 journal publication.
Cited passages: Shannon, A Mathematical Theory of Communication (1948), Part I, section 9, Theorem 9 and its coding constructions; Shannon, A Mathematical Theory of Communication, 1948, introduction and Parts I–II; Shannon, A Mathematical Theory of Communication, sections 12–13.
Published in The Bell System Technical Journal 27,379–423 and623–656.
Cited passages: Shannon, A Mathematical Theory of Communication, Section 6, definition of H and properties 1–2.
By Richard P. Stanley. The author-hosted title page identifies this as the second-edition version dated 15 July 2011. The date describes this draft, rather than the publication date of another printed edition.
Cited passages: §1.7, Proposition 1.7.1 and equation (1.67), printed pp. 61–62, refine multiset enumeration by a statistic and give the polynomial recurrence; Proposition 1.7.2, pp. 63–64, counts subspaces over a finite field by ordered independent vectors; Proposition 1.7.3 and Figures 1.14–1.15, pp. 64–66, connect row-reduced matrices, diagrams in a rectangle, and paths. PDF page numbers are one greater than these printed numbers. The title page is PDF page 1.
Cited passages from existing articles: Stanley, Enumerative Combinatorics, volume 1, section 1.7, Ferrers and Young diagrams; Stanley, Enumerative Combinatorics, volume 1, section 1.7, definitions of partitions and diagrams; Stanley, Enumerative Combinatorics, volume 1, section 1.8, conjugation and partition generating functions; Stanley, Enumerative Combinatorics, volume 1, section 1.9: Twelvefold Way entry 3; Stanley, Enumerative Combinatorics, volume 1, section 1.9: set partitions and their blocks; Stanley, Enumerative Combinatorics, volume 1, sections 1.1 and 2.1.
Published in Commentarii academiae scientiarum Petropolitanae.
Cited passages: Solutio problematis ad geometriam situs pertinentis, §§6, 9, 20.
Cited passages: Euler Archive, E53: written date, publication date, original source citation.
Collection of sources; individual chapter authors and dates are recorded below.
Cited passages: Lecture 6, p. 1, Theorem 1.1.2(a) and isolated-vertex note; p. 2, trivial trail convention; Lecture 6, pp. 1–3, Theorem 1.1.2 and the note about isolated vertices.
Published in Proceedings of the IRE.
Cited passages: David A. Huffman, A Method for the Construction of Minimum-Redundancy Codes, p. 1099, Derived Coding Requirements: equal-probability messages may have unequal lengths and may exchange codes without changing the mean; David A. Huffman, A Method for the Construction of Minimum-Redundancy Codes, p. 1099: Derived Coding Requirements and Optimum Binary Code.
Cited passages: Ben Lynn, Symbol Codes, Huffman section: leaf exchanges and reduction to a composite symbol; Ben Lynn, Symbol Codes, Huffman section: the identity L(C,X)=L(C',X')+p0+p1 and the replacement-code contradiction; Ben Lynn, Symbol Codes: expected-length definition and Huffman section.
Published in the Institute of Radio Engineers International Convention Record, volume 7 (1959). The introductory summary fixes a nonnegative letter-reconstruction cost and an allowed average distortion, then studies the equivalent source rate.
Accompanying implementation by Robert Sedgewick and Kevin Wayne, explicitly credited by the source file’s author tags, for Algorithms, 4th edition by Robert Sedgewick and others. GitHub hosts the inspected source. The textbook publication year is 2011; no source-file publication date is established, and the copyright range is a separate date role.
Inspected locators: class documentation and author tags; constructor; relax and check methods; textbook attribution footer. This is the queue implementation.
Cited passages: BipartiteX.java, class documentation: breadth-first search, linear construction time and vertex-linear extra space; bfs method: odd-cycle reconstruction; BipartiteX.java, constructor component loop and bfs method: discovery colours, parent pointers and same-colour conflict.
Authored accompanying software by Robert Sedgewick and Kevin Wayne, identified by the implementation bylines. The book publication year is 2011; copyright 2002–2025 is not an implementation publication date. Implementation locators refer to the inspected source file, not to the textbook pages.
Cited passages: Graph.java, class documentation and fields: vertex-indexed adjacency collections; addEdge: entries at both endpoints; Graph.java, class documentation: parallel edges and two-entry undirected self-loop convention; addEdge applies both insertions even when v equals w.
Authored accompanying software by Robert Sedgewick and Kevin Wayne, identified by the implementation bylines. The book publication year is 2011; copyright 2002–2025 is not an implementation publication date. Implementation locators refer to the inspected source file, not to the textbook pages.
Cited passages: Digraph.java, addEdge, adj and outdegree: one entry in the tail's collection; indegree is maintained separately; Digraph.java, class documentation and addEdge: parallel edges permitted; a directed self-loop adds one outgoing entry and increments indegree once; Digraph.java, class documentation and adj: obtaining the collection versus iterating in time proportional to outdegree.
Accompanying software for Algorithms, 4th edition by Robert Sedgewick and others, authored by Robert Sedgewick and Kevin Wayne, both named in the implementation bylines. GitHub hosts their algs4 repository. The footer gives 2011 as the textbook publication year; its copyright interval does not date the implementation. These locators refer to the inspected software rather than to textbook pages.
Cited passages: Browser lines 0–3: class documentation, directed endpoints, real-valued capacity and flow, @author declarations.; Browser lines 4–6: constructors enforce nonnegative capacity and flow bounded between zero and capacity.; Browser lines 11–13: actual residualCapacityTo and addResidualFlowTo bodies distinguish forward capacity-minus-flow and backward flow.; Browser lines 14–16: footer credits whole-book authors, publisher and 2011 publication year..
Accompanying software for Algorithms, 4th edition by Robert Sedgewick and others, authored by Robert Sedgewick and Kevin Wayne, both named in the implementation bylines. GitHub hosts their algs4 repository. The footer gives 2011 as the textbook publication year; its copyright interval does not date the implementation. These locators refer to the inspected software rather than to textbook pages.
Cited passages: Lines 12–35: maximum-flow/minimum-cut purpose and explicit implementation authors.; Lines 138–177: excess computes incoming minus outgoing edge amounts; isFeasible checks capacity constraints and conservation at nonterminal vertices.; Lines 180–209: check verifies feasibility, s-in/t-out membership, forward-only cut capacity sum and equality with flow value.; Lines 246–252: copyright interval and accompanying book authors, publisher, 2011 publication year..
Accompanying software for Algorithms, 4th edition by Robert Sedgewick and others, authored by Robert Sedgewick and Kevin Wayne, as credited in the implementation. GitHub hosts the author repository. The footer identifies 2011 as textbook publication; no implementation publication or revision date is established.
Cited passages: class documentation lines 39–68: signed weights, ties, minimum spanning forest, union-find, sorting complexity, author tags; constructor lines 79–100: sort, representative queries, merges, n-1 stopping condition; footer lines 194–199: textbook metadata.
Accompanying software for Algorithms, 4th edition by Robert Sedgewick and others, authored by Robert Sedgewick and Kevin Wayne, as credited in the implementation. GitHub hosts the author repository. The footer identifies 2011 as textbook publication; no implementation publication or revision date is established.
Cited passages: class documentation lines 13–60: partition, representatives, operations, union by size without path compression, logarithmic operation bound and authors; union method lines 135–148: smaller root attaches below larger root.
Accompanying software for Algorithms, 4th edition by Robert Sedgewick and others, credited to Robert Sedgewick and Kevin Wayne in its author declarations. GitHub hosts the author repository. The footer’s 2011 date identifies the textbook publication; the software has no established publication or revision date.
Cited passages: class documentation, lines 25–77; constructor, lines 92–100; find, lines 109–115; union, lines 149–160. The implementation uses path compression by halving.
The inspected PDF carries an October 20, 2022 production timestamp and a title page naming both authors. Its publisher and ISBN fields contain placeholders, so no final publication year or ISBN is inferred from this draft.
Cited passages: §16.1, Corollary 16.2 and equation (16.2), printed pp. 261–262: the optimal fixed-prior Bayesian error exponent. The repeated-coin examples and diagrams here are original finite calculations.
Publisher: ETH Zürich (official lecture-slide host).
Cited passages: Line graphs and edge coloring, slide 1: arbitrary labeling versus proper edge coloring; Line graphs and edge coloring, slide 1: line graph identity; Line graphs and edge coloring, slide 2: bipartite multigraph equality, multiplicity bound and fat triangle.
Publisher: IEEE.
Published in IEEE Transactions on Information Theory, 44(6), 2505–2523.
Retrospective account is qualified as the author's assessment; no absolute first-priority claim. PDF equations mostly absent in text extractor; elementary counts and coarse polynomial/exponential bounds also checked independently. DOI omitted because primary DOI metadata was not inspected.
Published in IBM Journal of Research and Development, volume 4, pp. 66–82, January 1960.
Publisher: MIT OpenCourseWare.
Lecture 5f of MIT 6.042J and 18.062J, Mathematics for Computer Science, dated 7 October 2005. Authorship is credited to this slide deck, rather than to every resource in the course.
Cited passages: Planar Graphs; Bipartite Matching, slide lec 5f.6, including the outer face; Planar Graphs; Bipartite Matching, slides lec 5f.14–5f.15; Planar Graphs; Bipartite Matching, slides lec 5f.3 and 5f.12.
Publisher: MIT OpenCourseWare (official distribution).
The inspected online textbook is dated 18 May 2015; this is a version date, rather than a claim about first publication.
Cited passages: Lehman, Leighton and Meyer, Mathematics for Computer Science, Definition 11.7.1; Lehman, Leighton and Meyer, Mathematics for Computer Science, §11.8.1: cycles and backtracking; Lehman, Leighton and Meyer, Mathematics for Computer Science, §11.8.1: length-zero convention; Lehman, Leighton and Meyer, Mathematics for Computer Science, §§9.2 and 11.8.1: closed walks; Mathematics for Computer Science, §12.4, Lemma 12.4.1, printed p. 485; Mathematics for Computer Science, §12.4, Lemma 12.4.2 and Theorem 12.4.3, printed pp. 485–486; Mathematics for Computer Science, §12.5, Lemma 12.5.2 and Theorem 12.5.3, printed pp. 486–487.
Additional cited passages in the 18 May 2015 revision: §5.2.1, printed p. 125; §5.2.2, printed pp. 125–126; §5.3, printed pp. 129–130. The title page credits the same three whole-book authors; the date is a revision/version date.
Publisher: Operations Research Society of America (original); INFORMS (current archive).
Published in Journal of the Operations Research Society of America 2(4), pp. 393–410.
Cited passages: Solution of a Large-Scale Traveling-Salesman Problem by G. Dantzig, R. Fulkerson and S. Johnson, abstract; Journal of the Operations Research Society of America 2(4), pp. 393–410 (1954).
Publisher: Trinity College Dublin (archive host).
Cited passages: The Icosian Calculus, Hamilton papers archive: opening historical introduction and quoted report of the 1857 British Association presentation: dodecahedron projection and ivory pins.
Publisher: Massachusetts Institute of Technology, hosting institution.
Date printed on these standalone authored lecture notes; not a verified book publication year.
Cited passages: Michel X. Goemans, Matroid optimization, section 5.1, p. 1, axioms (I1) and (I2); Michel X. Goemans, Matroid optimization, section 5.1, p. 1, maximal independent sets and bases; Michel X. Goemans, Matroid optimization, section 5.2, pp. 5–6, greedy procedure and theorem 5.2.
Lecture dated 11 February 2020 for Statistics 36-462/662, Spring 2020. The course page identifies Cosma Rohilla Shalizi as professor, without providing a separate slide byline.
Cited passages: Information Theory I — Scene Setting and Statistical Applications, Lecture 9, section Conditional independence and conditional mutual information: conditional factorization and predictive irrelevance.
Publisher: David R. MacIver's Blog.
In Theory and Applications of Satisfiability Testing – SAT 2020, Lecture Notes in Computer Science 12178, pp. 201–217.
Publisher: Springer.
Published in 23rd Conference on Theory and Applications of Satisfiability Testing, SAT 2020.
Cited passages: §4.1, Proposition 1 and proof, manuscript pp. 6–7; §4.1, manuscript pp. 5–6, construction steps 1–3.
Publisher: National Academy of Sciences.
Published in Proceedings of the National Academy of Sciences of the United States of America.
Cited passages: Claude Berge, Two theorems in graph theory, printed p. 842: finite unoriented graph and Problem 3; printed p. 843, Theorem 1: maximum matching and absence of an alternating chain between neutral points.
Proceedings of the National Academy of Sciences 43(9), pp. 842–844; published 15 September 1957. The paper was communicated on 8 July 1957.
Publisher: Elsevier Science Publishing Co., Inc.
Published in Linear Algebra and Its Applications 114/115, 589–602.
Cited passages: Hassin and Megiddo (1989), Theorem 2.6 proof, printed p. 592: cycle orientation and contraction, explicitly described as a different constructive proof from Robbins's; Hassin and Megiddo, On Orientations and Shortest Paths (1989), printed pp. 591–592: bridge-connectedness, strong connectivity and Theorem 2.6 (Robbins).
Authored problem collection. The inspected cover is dated 18 August 2009; this identifies the supplied version rather than a book publication date. The Catalan interpretations occur in §5, printed pp. 38–39, Problems 153–159.
Cited passages: §5, Problem 154, printed p. 38: binary parenthesizations of n+1 letters; §5, printed pp. 38–39, formula (7) and Problems 154–159: Catalan counts, binary parenthesizations, binary trees and Dyck paths.
Standalone historical preprint, arXiv:1408.5711. Version 1 was submitted on 25 August 2014; the inspected version 2 is dated 27 August 2014. Its cover says the account will appear as an appendix in a forthcoming book by Richard P. Stanley; the authorship here applies to this preprint, not to the whole book.
Cited passages: §§2–3 and §5, printed pp. 2–4: Euler correspondence, Segner recurrence and Catalan's bracketed products.
Published in Nieuw Archief voor Wiskunde, series 5, volume 17, number 4, pp. 275–280.
Cited passages: Robbert Fokkink, Wie weet wie Willem Wijthoff was?, Nieuw Archief voor Wiskunde 5/17(4), December 2016, printed p. 279, Wythoffs bewijs van de stelling van Mantel: attribution of problem 28 in 1907.
Whole-book author: Oscar Levin. No separate chapter author is credited in the inspected section.
The author's institutional publication list dates the third edition to 2018. The online front matter displays 12 August 2025 without identifying that date as the edition's original publication date.[ref] [ref]
Cited passages: §1.2, Lattice Paths, step-position encoding; Binomial Coefficients, counting interpretations and recurrence; Pascal’s Triangle, indexing and edge values. The third edition’s 2018 publication year is distinct from the online front matter’s displayed date of 12 August 2025.
Cited passages: Discrete Mathematics: An Open Introduction, 3rd edition, §3.1 Truth Tables: conjunction, disjunction and negation tables; §3.1 Logical Equivalence: definition and comparison of truth-table columns; §3.1 Example 3.1.3 and De Morgan’s Laws box; Front Matter: title, whole-book author, edition, displayed date August 12, 2025; Institutional Oscar Levin profile, Publications entry: third edition (2018).
By Joseph Bernard Kruskal, printed as Joseph B. Kruskal, Jr. Published in Proceedings of the American Mathematical Society 7(1), 48–50, February 1956. Received 11 April 1955.
Cited passages: printed pp. 48–50, especially Construction A on p. 49 and the exchange argument on p. 50.
By David Gale and Lloyd Shapley, credited as D. Gale and L. S. Shapley. Published in The American Mathematical Monthly 69(1), 9–15 (January 1962). The 2018 publisher online date concerns digitization, not original publication. The University of Toronto hosts the inspected scan; hosting does not establish authorship.
Cited passages: §3, printed p. 11, deferred acceptance; §5, printed p. 14, Theorem 2 and rejection induction.
Sections 1, 4–5, enumeration with inherited exclusions.
Publisher text in the institutional repository: www.i-repository.net/contents/osakacu/sugaku/111F0000002-01203-15.pdf
Osaka Journal of Mathematics12(3),737–744,1975. Cited passage: Theorem3, printed pages741–742, the intersection-number upper bound for a uniform set family.
By Will Sawin. Primary preprint arXiv:2211.11504, version3 (19 June 2023): arxiv.org/abs/2211.11504v3
Theorems1–2 and their proofs give the golden-ratio frequency bound through entropy growth for independent unions. The nontrivial-family application requires a nonempty union; singleton families containing a nonempty set satisfy the bound directly.
By Nicolaas Govert de Bruijn and Paul Erdős. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen51,1277–1279 (also Indagationes Mathematicae10,421–423). Primary scan: users.renyi.hu/~p_erdos/1948-01.pdf
Theorem1 gives the finite unique-pair line-count bound and identifies the near-pencil and projective-plane equality configurations.
By George Pólya. Acta Mathematica68,145–254. DOI: doi.org/10.1007/BF02546665
ChapterI, §16, printed page163, states the general cycle-index substitution theorem; the introduction motivates enumeration by rotations and chemical structures.
§2, printed pages4–5, fixes the Entringer first-entry/down-up convention and its recurrence and triangular array.
By Richard P. Stanley and John R. Stembridge. Journal of Combinatorial Theory, SeriesA62,261–279. Author-hosted primary article: math.mit.edu/~rstan/pubs/pubfiles/87.pdf
§1, equation(1.1), defines the Jacobi-Trudi matrix and its Schur determinant. §3, printed page270, explicitly fixes the unsigned forgotten-function convention, in contrast to the signed convention used by some sources.
Theorem1 reports a seven-point non-Ramsey configuration on a circle for every transcendental parameter r>2. The source is a preprint; its first-page disclosure and author note distinguish the main result from further appendix claims. The spherical-point-set entry attributes the reported counterexample to this dated preprint rather than asserting an undated open status.
Definition1.5 and Theorem1.6 specify the positive-coefficient separated-block systems and their monochromatic sum subsystems; Theorem1.4 states the underlying Milliken-Taylor theorem.
By Neil Hindman, Imre Leader and Dona Strauss. Proceedings of the Edinburgh Mathematical Society46,45–61. DOI: doi.org/10.1017/S001309150200010X
Author-hosted final manuscript: nhindman.us/research/separate.pdf
Definition1.5 and Theorem1.7 give compression and the positive-rational-proportionality criterion for simultaneously monochromatic positive-coefficient systems.
The paragraph before Corollary1.7, printed p.5, recalls the ordinary Ramsey lower bound for a graph containing a subgraph of minimum degree d.
Section1, equation1, defines the homomorphism-density inequality. Its graph specialization quantifies over all host graphons.
Published in Ergodic Theory of Z-d-actions, London Mathematical Society Lecture Note Series 228, pp. 1–61.
Theorem 1.2 and section 4 state and prove the abelian sum-and-difference bound, with the minimal-growth proof in section 2.
Sections 2.3–2.6 discuss uniformity norms and phase detection. Section 3, particularly Corollary 3.5, treats norms generated by spanning test families and their duals; section 4 develops dense-model transference.
Author's manuscript, revised October 2013: arxiv.org/abs/1111.6453
Section 2.1 defines a finite ground set; Proposition 2.2 in Section 2.2 proves the equivalent first-difference formulation of submodularity.
Section 1.1 specifies counting convolution and counting Lp norms; propositions 1.1 and 1.3 state local almost-periodicity; section 3 gives the sampling proof, and section 9.1 discusses functions.
Theorem 2, page 2, is the functional Croot-Sisask lemma; section 2 fixes counting Lp norms and averaging convolution with a normalized indicator, and section 4 gives its moment/sampling proof.
Computational Complexity 6, 312–340. DOI: 10.1007/BF01270385. Author-hosted article; Section 2 commute-time identity. Primary publisher metadata distinguishes journal year 1996 from the preliminary 1989 conference version. Reuse existing source authors where live; new authors/Works EMPTY proposals only.
By James L. Massey. Published in IEEE Transactions on Information Theory 15(1), pages 122–127.
Sections II–III develop minimal-register synthesis and the Berlekamp-Massey algorithm; Sections IV–V apply it to BCH code decoding.
By Michael J. Whinihan. The Fibonacci Quarterly 1(4), pages 9–13, December 1963.
Pages 9–12 give the rules and the least-Zeckendorf-summand winning strategy for Fibonacci Nim.
By A. J. Cole, A. J. T. Davie. The Mathematical Gazette 53(386), pages 354–357, December 1969.
Introduces Euclid game. The wiki specifies its own terminal convention explicitly rather than assuming that all variants agree.
Cited passages: Appendix A, equations (A.10)–(A.13), printed pp. 26–27: entropy of group sums, entropic Ruzsa distance and triangle inequality. The inspected version is arXiv:2311.05762v2 (12 December 2023), in characteristic two.
Cited passages: Section 8.4, Margulis–Russo Formula, equations (8.8)–(8.9), printed pp. 224–225: derivative and biased-influence normalization. The book originally appeared in April 2014; the cited freely available edition is arXiv:2105.10386v1.
Cited passages: Sections 14–15, printed pp. 691–695, especially the discussion following Figure 7: random-cipher equivocation approaches zero sharply and defines an approximate unicity distance; section 15 lists corrections for actual ciphers. Published in Bell System Technical Journal 28(4), pp. 656–715, DOI 10.1002/j.1538-7305.1949.tb00928.x.
Author lecture notes, 6 April 2009. Definition 1 defines omega-Jónsson functions; Theorem 2 states their existence assuming choice and presents the Galvin–Prikry argument.
Computer Vision, Graphics, and Image Processing 35(3), 283–305. Publisher record: www.sciencedirect.com/science/article/pii/0734189X86900022 . Author and bibliographic metadata verified from the indexed publisher record; full text unavailable. Cited for the research/expository contribution; the profiles explain basic set-operation examples directly.
Verified locator: Preface, sections 1.3–1.5: linear patterns, finite-field polynomial phases and Gowers norms.
Verified locator: ICM 2010, section 1 and section 4.2: minimum distance, list output and Reed-Solomon interpolation.
Verified locator: IIT Guwahati Theory of Computation course, Chomsky Hierarchy module 14 lecture 1: two simulation theorems. Search-indexed technical text; direct HTML uses image-rendered mathematics.
Author-hosted manuscript dated 17 June 2004. Introduction defines the cost ratio for the best Nash equilibrium and explains the stable-recommendation interpretation.
Verified locator: Project-maintained binary Golay entry, Description and perfect-code properties; ternary and extended parameters verified at errorcorrectionzoo.org/c/ternary_golay .
Original FOCS 2000 paper, primary byline. Introduction and routing model: nonatomic routing, total latency and inefficiency bounds. This conference version is distinct from the later journal version.
Articles were limited to the first 100 out of 104 total.

Ancestors (3)

  1. Mathematics bibliography
  2. Mathematics
  3. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version