Between graphical zonotope and graph-associahedron

2022/09/24 by Pešović, Marko, Stojadinović, Tanja
#05C22 #16T05 #52B11 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.12053

Abstract

This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs.

Related

• Hopf monoids and generalized permutahedra
• Upper and lower bound theorems for graph-associahedra
• Faces of Generalized Permutohedra
• Acyclotopes and Tocyclotopes
• Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra