By James L. Massey. Published in IEEE Transactions on Information Theory 15(1), pages 122–127.

Author's institutional archive: www.isiweb.ee.ethz.ch/archive/massey_pub/pdf/BI411.pdf

Sections II–III develop minimal-register synthesis and the Berlekamp-Massey algorithm; Sections IV–V apply it to BCH code decoding.

By Ashok K. Chandra, Prabhakar Raghavan, Walter L. Ruzzo, Roman Smolensky, Prasoon Tiwari.

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.

Author-hosted notes: khenriot.wordpress.com/wp-content/uploads/2016/03/almostp1.pdf

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.

Original author manuscript: ecroot.math.gatech.edu/prob-almost-periods.pdf

Preprint record: arxiv.org/abs/1003.2978

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.

By Francis Bach.

Author's project page: www.di.ens.fr/~fbach/submodular/

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.

Author preprint: arxiv.org/abs/0811.3103v1

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 preprint: arxiv.org/abs/1101.3507v3

Theorem 1.2 and section 4 state and prove the abelian sum-and-difference bound, with the minimal-growth proof in section 2.

By Vitaly Bergelson.

Published in Ergodic Theory of Z-d-actions, London Mathematical Society Lecture Note Series 228, pp. 1–61.

Author-hosted text: people.math.osu.edu/bergelson.1/ertupdatenov6.pdf

Publication details: Author's publication list, first entry

Section1, equation1, defines the homomorphism-density inequality. Its graph specialization quantifies over all host graphons.

The paragraph before Corollary1.7, printed p.5, recalls the ordinary Ramsey lower bound for a graph containing a subgraph of minimum degree d.

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.

By Vitaly Bergelson, Neil Hindman and Kendall Williams. Author-hosted primary manuscript: people.math.osu.edu/bergelson.1/BHW_PolynomialMT.pdf

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.

Primary preprint arXiv:2609.23327v1: arxiv.org/abs/2609.23327v1

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.

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.

By Richard P. Stanley. Preprint arXiv:0912.4240: arxiv.org/abs/0912.4240

Author-hosted text: math.mit.edu/~rstan/papers/altperm.pdf

§2, printed pages4–5, fixes the Entringer first-entry/down-up convention and its recurrence and triangular array.

By George Pólya. Acta Mathematica68,145–254. DOI: doi.org/10.1007/BF02546665

Primary scan: archive.ymsc.tsinghua.edu.cn/pacm_download/117/5571-11511_2006_Article_BF02546665.pdf

ChapterI, §16, printed page163, states the general cycle-index substitution theorem; the introduction motivates enumeration by rotations and chemical structures.

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 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.

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 D. Hugh Redelmeier.

Primary source: barequet.cs.technion.ac.il/poly-papers/math-cs/1981-Redelmeier.pdf

Sections 1, 4–5, enumeration with inherited exclusions.