Séminaire Lotharingien de Combinatoire, 89B.87 (2023), 7 pp.
Shiyue Li
Equivariant Log-Concavity of Independence Sequences of Claw-Free Graphs
Abstract.
We show that the graded vector space spanned by independent vertex sets of any claw-free graph is strongly equivariantly log-concave, viewed as a graded permutation representation of the graph automorphism group. Our proof reduces the problem to the equivariant hard Lefschetz theorem on the cohomology of a product of projective lines, inspired by a combinatorial map of Krattenthaler. Both the result and the proof generalize our previous result on graph matchings. This also gives a strengthening and a new proof of results of Hamidoune, and Chudnovsky-Seymour.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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