Convex Polytopes from Nested Posets

TL;DR

This paper introduces a new family of convex polytopes derived from nested posets, generalizing known structures like graph associahedra and nestohedra, with implications for combinatorial and geometric theory.

Contribution

It defines a novel class of convex polytopes based on nested posets, expanding the framework beyond generalized permutohedra and connecting to complex combinatorial structures.

Findings

New family of simple convex polytopes from nested posets

Generalization of graph associahedra and nestohedra

Distinct from generalized permutohedra

Abstract

Motivated by the graph associahedron KG, a polytope whose face poset is based on connected subgraphs of G, we consider the notion of associativity and tubes on posets. This leads to a new family of simple convex polytopes obtained by iterated truncations. These generalize graph associahedra and nestohedra, even encompassing notions of nestings on CW-complexes. However, these poset associahedra fall in a different category altogether than generalized permutohedra.