Generalized Rook Polynomials

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 establishedwith absoluteStirling numbersand 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. Dedicated to the memory of Gian-Carlo Rota, friend and inspiring colleague

• Type: Journal
• Year: 2000
• Where: JCT
• Authors: Jay Goldman, James Haglund
• Keywords: AbsoluteStirling Numbersand Permutations, JCT 2000, Polynomial, Rook Polynomials