Speaker: Liu Li, professor and doctoral supervisor, Qufu Normal University

Date: May 24, 2025

Time: 10:00-11:00 am

Location: E119, Huagang East Building, Shandong University Qingdao Campus

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences, Shandong University

Abstract:

In this paper, we construct multivariate generalizations of the Eulerian polynomials, the type $B$ analogues and the $r$-colored Eulerian polynomials for restricted exceedance statistics by using context-free grammars. Moreover, the grammars enable us to obtain the combinatorial interpretations and the recurrence relations for these multivariate polynomials in terms of permutations on the symmetric group, the hyperoctahedral group, the wreath product of cyclic group and symmetric group. Based on a sufficient condition for the real stability of recurrence multivariate sequences of polynomials, we obtain the real stability of these multivariate polynomials. As applications, we show the real-rootedness of the univariate Eulerian polynomials, type $B$ analogues and $r$-colored Eulerian polynomials for restricted exceedance statistics.

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https://www.view.sdu.edu.cn/info/1020/202494.htm