Valuations and the Hopf Monoid of Generalized Permutahedra
Valuations and the Hopf Monoid of Generalized Permutahedra
Abstract The goal of this paper is to show that valuation theory and Hopf theory are compatible on the class of generalized permutahedra. We prove that the Hopf structure $\textbf {GP}^+$ on these polyhedra descends, modulo the inclusion-exclusion relations, to an indicator Hopf monoid $\mathbb {I}(\textbf {GP}^+)$ of generalized permutahedra …