1997/06/18 by James Haglund, Haglund, James
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.math/9706219
openalex publication_date 1997/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Connections between q-rook polynomials and matrices over finite fields are exploited to derive a new statistic for Garsia and Remmel's q-hit polynomial. Both this new statistic mat and another statistic for the q-hit polynomial ξ recently introduced by Dworkin are shown to induce different multiset Mahonian permutation statistics for any Ferrers board. In addition, for the triangular boards they are shown to generate different families of Euler-Mahonian statistics. For these boards the ξ family includes Denert's statistic den, and gives a new proof of Foata and Zeilberger's Theorem that (exc,den) is jointly distributed with (des,maj). The mat family appears to be new. A proof is also given that the q-hit polynomials are symmetric and unimodal.