Falling Factorials, Generating Functions, and Conjoint Ranking Tables

Brad Osgood; William Wu

Falling Factorials, Generating Functions, and Conjoint Ranking Tables

Combinatorics 2009-12-01 v1

Authors: Brad Osgood , William Wu

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.

Keywords

combinatorics functors in category theory special functions

Cite

@article{arxiv.0810.3327,
  title  = {Falling Factorials, Generating Functions, and Conjoint Ranking Tables},
  author = {Brad Osgood and William Wu},
  journal= {arXiv preprint arXiv:0810.3327},
  year   = {2009}
}

Comments

15 pages, 3 figures

Falling Factorials, Generating Functions, and Conjoint Ranking Tables

Abstract

Keywords

Cite

Comments

Related papers