The \mathbf{s}-Eulerian polynomials have only real roots

Our object of study is the generating polynomial of the statistic over the set of \mathbf {s}-inversion sequences of length n. Since this ascent statistic over inversion sequences is equidistributed with the descent statistic over permutations, we call this generalized polynomial the . The main resu...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2015-02, Vol.367 (2), p.1441
Main Authors: Carla D. Savage, Mirkó Visontai
Format: Article
Language:English
Online Access:Get full text
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Summary:Our object of study is the generating polynomial of the statistic over the set of \mathbf {s}-inversion sequences of length n. Since this ascent statistic over inversion sequences is equidistributed with the descent statistic over permutations, we call this generalized polynomial the . The main result of this paper is that, for any sequence \mathbf {s} of positive integers, the \mathbf {s}-Eulerian polynomial has only real roots.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2014-06256-9