Shellability of Kohnert posets

In this paper, we are concerned with identifying, among the family of posets associated with Kohnert polynomials, those whose order complex has a certain combinatorial property. In particular, for numerous families of Kohnert polynomials, including key polynomials, we determine when the associated K...

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Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 12; p. 114707
Main Authors Kerr, Celia, Mayers, Nicholas W., Russoniello, Nicholas
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Subjects
Key polynomials
Kohnert polynomials
Kohnert posets
Shellablility
Key polynomials
Kohnert polynomials
Shellablility
Kohnert posets
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Summary:In this paper, we are concerned with identifying, among the family of posets associated with Kohnert polynomials, those whose order complex has a certain combinatorial property. In particular, for numerous families of Kohnert polynomials, including key polynomials, we determine when the associated Kohnert posets are shellable. Moreover, we find that when such posets are shellable, they have the stronger property of being EL-shellable. Interestingly, under certain diagram restrictions, shellability of a Kohnert poset is equivalent to multiplicity-freeness of the associated Kohnert polynomial.
ISSN:0012-365X
DOI:10.1016/j.disc.2025.114707