Some applications of Rees products of posets to equivariant gamma-positivity
| Autor: | Christos A. Athanasiadis |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Mathematics::Combinatorics Mathematics::Commutative Algebra Group (mathematics) Homology (mathematics) 05E18 05E45 05E05 06A07 Symmetric function Graded poset Product (mathematics) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Equivariant map Combinatorics (math.CO) Geometric combinatorics Partially ordered set Mathematics |
| Zdroj: | Algebraic Combinatorics. 3:281-300 |
| ISSN: | 2589-5486 |
| DOI: | 10.5802/alco.85 |
| Popis: | The Rees product of partially ordered sets was introduced by Bj\"orner and Welker. Using the theory of lexicographic shellability, Linusson, Shareshian and Wachs proved formulas, of significance in the theory of gamma-positivity, for the dimension of the homology of the Rees product of a graded poset $P$ with a certain $t$-analogue of the chain of the same length as $P$. Equivariant generalizations of these formulas are proven in this paper, when a group of automorphisms acts on $P$, and are applied to establish the Schur gamma-positivity of certain symmetric functions arising in algebraic and geometric combinatorics. Comment: Final version, with a section on type B Coxeter complexes added; to appear in Algebraic Combinatorics |
| Databáze: | OpenAIRE |
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