Convex Polytopes from Nested Posets
Satyan L. Devadoss, Stefan Forcey, Stephen Reisdorf, Patrick Showers

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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
