226 research outputs found
-Rook polynomials and matrices over finite fields
Connections between -rook polynomials and matrices over finite fields are
exploited to derive a new statistic for Garsia and Remmel's -hit polynomial.
Both this new statistic and another statistic for the -hit polynomial
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 family includes Denert's
statistic , and gives a new proof of Foata and Zeilberger's Theorem that
is jointly distributed with . The family appears
to be new. A proof is also given that the -hit polynomials are symmetric and
unimodal
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