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. Connecti ons are established with absolute Stirling numbers and permutations, Bessel polynomials, matchings, multiset permutations, hypergeometric functions, A bel polynomials and forests, and polynomial sequences of binomial type. Fac torization and reciprocity theorems are proved and a q-analogue is given. ( C) 2000 Academic Press.