Equivariant log-concavity of graph matchings
Combinatorics
2026-04-08 v2
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.
Cite
@article{arxiv.2202.08828,
title = {Equivariant log-concavity of graph matchings},
author = {Shiyue Li},
journal= {arXiv preprint arXiv:2202.08828},
year = {2026}
}
Comments
8 pages; v2, improved and corrected, final version accepted at AlCo