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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Published in: | Transactions of the American Mathematical Society 2015-02, Vol.367 (2), p.1441 |
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Main Authors: | , |
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. |
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ISSN: | 0002-9947 1088-6850 |
DOI: | 10.1090/S0002-9947-2014-06256-9 |