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- W4288602013 abstract "The binomial Eulerian polynomials, introduced by Postnikov, Reiner, and Williams, are $gamma$-positive polynomials and can be interpreted as $h$-polynomials of certain flag simplicial polytopes. Recently, Athanasiadis studied analogs of these polynomials for colored permutations. In this paper, we generalize them to $mathbf{s}$-inversion sequences and prove that these new polynomials have only real roots by the method of interlacing polynomials. Three applications of this result are presented. The first one is to prove the real-rootedness of binomial Eulerian polynomials, which confirms a conjecture of Ma, Ma, and Yeh. The second one is to prove that the symmetric decomposition of binomial Eulerian polynomials for colored permutations is real-rooted. Thirdly, our polynomials for certain $mathbf{s}$-inversion sequences are shown to admit a similar geometric interpretation related to edgewise subdivisions of simplexes." @default.
- W4288602013 created "2022-07-29" @default.
- W4288602013 creator A5054926232 @default.
- W4288602013 creator A5088061652 @default.
- W4288602013 date "2019-02-04" @default.
- W4288602013 modified "2023-09-29" @default.
- W4288602013 title "Real-rootedness of variations of Eulerian polynomials" @default.
- W4288602013 doi "https://doi.org/10.48550/arxiv.1902.01278" @default.
- W4288602013 hasPublicationYear "2019" @default.
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