ALGEBRAIC COMBINATORICS

no. 1
Some applications of Rees products of posets to equivariant gamma-positivity
Athanasiadis, Christos A.1
1 Department of Mathematics National and Kapodistrian University of Athens Panepistimioupolis Athens 15784, Greece
Algebraic Combinatorics, Volume 3 (2020) no. 1, pp. 281-300.

The Rees product of partially ordered sets was introduced by Björner 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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.85
Classification: 05E05, 05E18, 05E45, 06A07
Keywords: Rees product, poset homology, group action, Schur gamma-positivity, local face module
Athanasiadis, Christos A. 1

1 Department of Mathematics National and Kapodistrian University of Athens Panepistimioupolis Athens 15784, Greece
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Athanasiadis, Christos A. Some applications of Rees products of posets to equivariant gamma-positivity. Algebraic Combinatorics, Volume 3 (2020) no. 1, pp. 281-300. doi : 10.5802/alco.85. https://alco.centre-mersenne.org/articles/10.5802/alco.85/

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