Between graphical zonotope and graph-associahedron

Authors: MARKO PESOVIC, TANJA STOJADINOVIC

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. In the last section, we study some properties related to $\mathcal{H}$-polytopes.

Keywords: Generalized permutohedron, quasisymmetric function, graph, decorated graph, combinatorial Hopf algebra, $f-$polynomial

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