Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $q$-Rook polynomials and matrices over finite fields   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.

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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: cond-mat