Work

Two Classes of Posets with Real-Rooted Chain Polynomials

Year: 2024

Type: article

Abstract: The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. It has been a challenging open problem to determine which posets have real-rooted chain polynomials. Two new classes of posets, namely those of all rank-selected subposets of Cohen-Macaulay simplicial posets and all noncrossing partition lattices associated to finite Coxeter groups, are shown to have this property. The first result generalizes one of Brenti and Welker. As a special case, the descent enumerator of permutations of the set $\{1, 2,\dots,n\}$ which have ascents at specified positions is shown to be real-rooted, hence log-concave and unimodal, and a good estimate for the location of the peak is deduced.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12218

Authors: Christos A. Athanasiadis, Theo Douvropoulos, Katerina Kalampogia-Evangelinou

Institutions: National and Kapodistrian University of Athens, Brandeis University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Hellenic Foundation for Research and Innovation

Award: G2281415621