Enumerative Combinatorics, Volume 1 (second-edition draft) by Richard Stanley (2011)

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.