Corpus ID: 237571565

Deformation cones of graph associahedra and nestohedra

@inproceedings{Padrol2021DeformationCO,
  title={Deformation cones of graph associahedra and nestohedra},
  author={Arnau Padrol and Vincent Pilaud and Germain Poullot},
  year={2021}
}
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 yields 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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References

SHOWING 1-10 OF 37 REFERENCES
Coxeter Complexes and Graph-Associahedra
Abstract Given a graph Γ , we construct a simple, convex polytope, dubbed graph-associahedra , whose face poset is based on the connected subgraphs of Γ . This provides a natural generalization ofExpand
ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras
A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitablyExpand
Realizations of the Associahedron and Cyclohedron
TLDR
Many different realizations with integer coordinates for the associahedron and cyclohedron are described and this settles a conjecture of N. Reading for cambrian lattices of these types. Expand
Generalized associahedra from the geometry of finite reflection groups
TLDR
Permutahedra and generalized associahedra are a class of convex polytopes arising naturally from the study of finite reflection groups, and the intimate links those two classes of poly topes share are presented. Expand
Which nestohedra are removahedra
A removahedron is a polytope obtained by deleting inequalities from the facet description of the classical permutahedron. Relevant examples range from the associahedra to the permutahedron itself,Expand
Compatibility fans for graphical nested complexes
TLDR
A compatibility degree is defined that the compatibility vectors of all tubes of a graph "$G$ with respect to an arbitrary maximal tubing on $G$ support a complete simplicial fan realizing the nested complex of $G$. Expand
Matroid polytopes, nested sets and Bergman fans
The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we presentExpand
Nested complexes and their polyhedral realizations
This note which can be viewed as a complement to Alex Postnikov's paper math.CO/0507163, presents a self-contained overview of basic properties of nested complexes and their two dual polyhedralExpand
ASSOCIAHEDRA FOR FINITE TYPE CLUSTER ALGEBRAS AND MINIMAL RELATIONS BETWEEN g-VECTORS
We show that the mesh mutations are the minimal relations among the g-vectors with respect to any initial seed in any finite type cluster algebra. We then use this algebraic result to deriveExpand
Faces of Generalized Permutohedra
The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f-, h- and γ- vectors. These polytopes include permutohedra, associahedra, graph- associahedra,Expand
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