Geodesic
Two classes of posets with real-rooted chain polynomials
Christos A. Athanasiadis1 ; Theo Douvropoulos2 ; Katerina Kalampogia-Evangelinou1
1National and Kapodistrian University of Athens
2Department of Mathematics, Brandeis University
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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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.
DOI : 10.37236/12218
Classification : 06A07, 05A15, 05E45, 26C10
Mots-clés : Cohen-Macaulay simplicial posets, real-rooted chain polynomials

Christos A. Athanasiadis  1   ; Theo Douvropoulos  2   ; Katerina Kalampogia-Evangelinou  1

1 National and Kapodistrian University of Athens
2 Department of Mathematics, Brandeis University 
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Christos A. Athanasiadis; Theo Douvropoulos; Katerina Kalampogia-Evangelinou. Two classes of posets with real-rooted chain polynomials. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12218

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