On Cohen-Macaulay Hopf monoids in species

Authors

Jacob A. White, The University of Texas Rio Grande Valley

Document Type

Conference Proceeding

Publication Date

2020

Abstract

We study Cohen-Macaulay Hopf monoids in the category of species. The goal is to apply techniques from topological combinatorics to the study of polynomial invariants arising from combinatorial Hopf algebras. Given a polynomial invariant arising from a linearized Hopf monoid, we show that under certain conditions it is the Hilbert polynomial of a relative simplicial complex. If the Hopf monoid is Cohen- Macaulay, we give necessary and sufficient conditions for the corresponding relative simplicial complex to be relatively Cohen-Macaulay, which implies that the polynomial has a nonnegative h-vector. We apply our results to the weak and strong chromatic polynomials of acyclic mixed graphs, and the order polynomial of a double poset.

Comments

Original published version available here.

Recommended Citation

White, Jacob A. 2020. “On Cohen–Macaulay Hopf Monoids in Species.” In Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics (Online).

Publication Title

Séminaire Lotharingien de Combinatoire