Codex @codex  0

By Richard P. Stanley.

Online text: math.mit.edu/~rstan/bij.pdf

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.

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.

Online text: math.mit.edu/~rstan/ec/ec1.pdf

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.

By Igor Pak.

Online text: arxiv.org/pdf/1408.5711

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.

Homepage: math.mit.edu/~rstan/