Q-Hit Polynomials Have Only Real Roots

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Doctor of Philosophy (PhD)
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Mathematics
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eulerian polynomials
Ferrers board
interlacing
q-hit polynomials
real-rooted
rook theory
Mathematics
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2016-11-29T00:00:00-08:00
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Abstract

We prove that Garsia and Remmel's q-hit polynomials for Ferrers boards have only real roots for fixed q > 0. This generalizes previous results by Haglund, Wagner and Ono [4] and Savage and Visontai [5]. We also extend the main recursion in [5] to hit polynomials for certain classes of Ferrers boards, which include the multiset Eulerian polynomials.

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James Haglund
Date of degree
2015-01-01
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