Falling Factorials, Generating Functions, and Conjoint Ranking Tables

Abstract

We investigate the coefficients generated by expressing the falling factorial $(xy{)}_k$ as a linear combination of falling factorial products $(x{)}_l(y{)}_m$ for $l,m=1,...,k$. Algebraic and combinatoric properties of these coefficients are discussed, including recurrence relations, closed-form formulae, relations with Stirling numbers, and a combinatorial characterization in terms of conjoint ranking tables.

15 pages, 3 figures

Cited by in corpus (1)

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