Deformation cones of graph associahedra and nestohedra

TL;DR

This paper characterizes the deformation cones of graph associahedra and nestohedra, extending classical results and introducing kinematic nestohedra that connect to scattering amplitudes.

Contribution

It provides a facet description of deformation cones for these polytopes, generalizing submodular function parametrizations and constructing new kinematic nestohedra.

Findings

Facet description of deformation cones for graph associahedra and nestohedra.

Generalization of the classical parametrization by submodular functions.

Introduction of kinematic nestohedra related to scattering amplitudes.

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.