Equivariant log-concavity of graph matchings

Abstract

For any graph, we show that the graded permutation representation of the graph automorphism group given by matchings is strongly equivariantly log-concave. The proof gives a family of equivariant injections inspired by a combinatorial map of Kratthenthaler and reduces to the hard Lefschetz theorem.

8 pages; v2, improved and corrected, final version accepted at AlCo

References in corpus (2)

• The categorical graph minor theorem
• On the equivariant log-concavity for the cohomology of the flag varieties