会议时间:2021 年 12 月 26 日, 8:50-16:40
腾讯会议 ID: 653-700-966
Antichain generating polynomials of posets
Abstract: This talk aims to introduce the conjectures made by Jian Ding and me in the draft posted as arXiv:1905.06692. We will focus on the antichain generating polynomials of [k] \timesQ, where Q is a connected minuscule poset classified by Proctor in 1984. The properties that we care about such polynomials include being gamma-positive,log-concave, palindromic and real-rooted.
gama-positivity of some combinatorial polynomials
Context-free grammars and unimodality
Abstract: In this talk, we give a short survey on the recent study of combinatorial structures by using context-free grammars. We shall discuss several refinements of Eulerian polynomials and second-order Eulerian polynomials. In particular, we discuss some unimodal polynomials.
Recent progress on the e-positivity of trees
Abstract: Motivated by Stanley and Stembridge’s 3+1 conjecture on the e-positivity of chromatic symmetric functions of certain graphs, and by Dahlberg, She, and van Willigenburg’s conjecture on the e-positivity of certain trees, we present in this talk the disordered phenomenon on the e-positivity of spider graphs of 3 legs.
Analytic aspects of graph polynomials
Abstract: Graph polynomials play an important role in the study of graph theory. In this talk, we discuss certain analytic properties of graph polynomials, with emphasis on the unimodality, log-concavity of coefficients and location of roots.
Statistics on Quasi-Stirling Permutations of Multisets and Partial Gama-Positivity
Abstract: In this talk, we will present some recent results on the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents, which generalizes several results obtained by Elizalde and solve two open problems posed by Elizalde. Moreover, we prove that the enumerative polynomials of quasi-Stirling permutations of multisets are partial gama-positive, thereby confirming a recent conjecture posed by Lin, Ma and Zhang.
Character immanants of combinatorial matrices
Abstract: Goulden and Jackson initiated the study of immanants of combinatorial matrices. In particular, they conjectured, and later Greene proved, that immanants of Jacobi-Trudi matrices are polynomials with nonnegative integer coefficients. Based on Greene's approach to Goulden and Jackson's conjecture, we further study the positivity of immanants of Giambelli-type matrices which were introduced by Hamel and Goulden, as well as the positivity of immanants of square submatrices of the Catalan-Stieltjes matrices and their associated Hankel matrices. In this talk, we will give an overview of related results. This is based on the joint work with Grace M.X. Li, Ethan Y.H. Li and Candice X.T. Zhang.
Unimodality problems of independence polynomials of graphs
Abstract: Unimodality problems often arise in combinatorics and other branches of mathematics. In this talk, we will introduce some results for unimodality of independence polynomials of graphs.