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Generalized Rook Polynomials

✍ Scribed by Jay Goldman; James Haglund

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
288 KB
Volume
91
Category
Article
ISSN
0097-3165

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✦ Synopsis

Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook polynomials. Connections are established with absolute Stirling numbers and permutations, Bessel polynomials, matchings, multiset permutations, hypergeometric functions, Abel polynomials and forests, and polynomial sequences of binomial type. Factorization and reciprocity theorems are proved and a q-analogue is given.

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