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- W4296975651 abstract "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 $xi$ 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 $xi$ 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." @default.
- W4296975651 created "2022-09-25" @default.
- W4296975651 creator A5088061652 @default.
- W4296975651 date "1997-06-17" @default.
- W4296975651 modified "2023-09-26" @default.
- W4296975651 title "$q$-Rook polynomials and matrices over finite fields" @default.
- W4296975651 doi "https://doi.org/10.48550/arxiv.math/9706219" @default.
- W4296975651 hasPublicationYear "1997" @default.
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