Deformation cones of graphical zonotopes

• Arnau Padrol ^[1] ; Vincent Pilaud ; Germain Poullot ^[1]
  1. [1] Pierre and Marie Curie University

     Pierre and Marie Curie University

     París, Francia

     
• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 217-223
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study deformations of graphical zonotopes. Deformations of the classical permutahedron (which is the graphical zonotope of the complete graph) have been intensively studiedin recent years under the name of generalized permutahedra. We provide an irredundantdescription of the deformation cone of the graphical zonotope associated to a graph G,consisting of independent equations defining its linear span (in terms of non-cliques of G)and of the inequalities defining its facets (in terms of common neighbors of neighbors in G).In particular, we deduce that the faces of the standard simplex corresponding to inducedcliques in G form a linear basis of the deformation cone, and that the deformation cone issimplicial if and only if G is triangle-free.