Séminaire Lotharingien de Combinatoire, 84B.45 (2020), 12 pp.

Jordan Almeter

Generalizing Nestohedra and Graph Associahedra for Simple Polytopes

Abstract. The graph associahedron is a simple polytope defined by associating a graph on n+1 vertices with the n+1 facets of a simplex in n dimensions, and truncating the faces of the simplex corresponding to connected subgraphs. The faces of this new polytope correspond to a lattice of tubings of the graph.

In this paper we generalize the graph associahedron by associating the vertices of graphs with the facets of simple polytopes, and truncating faces of the polytope based on connected subgraphs with restrictions. In the special case where the initial polytope is a hypercube, we examine connected subgraphs of graphs with positive and negative vertices. Certain graphs give us the permutahedron, the associahedron, the type Bn permutahedron, and polytopes conjectured to be of bi-Catalan combinatorial type.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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