2109.09200Sep 19, 202127 pages, 10 figures. Section 2 is adapted from Section 2.4 of arXiv:1906.06861v2 (and will disappear there)

Deformation cones of graph associahedra and nestohedra

Arnau Padrol, Vincent Pilaud, Germain Poullot

Combinatorics

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Abstract

We give the facet description of the deformation cones of graph associahedra and nestohedra, generalizing the classical parametrization of the family of deformed permutahedra by the cone of submodular functions. When the underlying building set is made of intervals, this leads in particular to the construction of kinematic nestohedra generalizing the kinematic associahedra that recently appeared in the theory of scattering amplitudes.

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