Authors: Curien, Pierre Louis
Obradović, Jovana 
Ivanović, Jelena
Title: Syntactic aspects of hypergraph polytopes
Journal: Journal of Homotopy and Related Structures
Volume: 14
Issue: 1
First page: 235
Last page: 279
Issue Date: 7-Mar-2019
Rank: M23
ISSN: 2193-8407
DOI: 10.1007/s40062-018-0211-9
This paper introduces an inductive tree notation for all the faces of polytopes arising from a simplex by truncations, which allows viewing face inclusion as the process of contracting tree edges. These polytopes, known as hypergraph polytopes or nestohedra, fit in the interval from simplices to permutohedra (in any finite dimension). This interval was further stretched by Petrić to allow truncations of faces that are themselves obtained by truncations. Our notation applies to all these polytopes. As an illustration, we detail the case of Petrić’s permutohedron-based associahedra. As an application, we present a criterion for determining whether edges of polytopes associated with the coherences of categorified operads correspond to sequential, or to parallel associativity.
Keywords: Categorification | Coherence | Operads | Polytopes
Publisher: Springer Link

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