Syntactic aspects of hypergraph polytopes

Syntactic aspects of hypergraph polytopes

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 per...

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Veröffentlicht in:Journal of homotopy and related structures 2019-03, Vol.14 (1), p.235-279
Hauptverfasser: Curien, Pierre-Louis, Obradović, Jovana, Ivanović, Jelena
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Sprache:eng
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Algebra
Algebraic Topology
Functional Analysis
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Number Theory
Polytopes
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Obradović, Jovana
Ivanović, Jelena
description 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.
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subjects Algebra
Algebraic Topology
Functional Analysis
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Number Theory
Polytopes
title Syntactic aspects of hypergraph polytopes
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