Coxeter submodular functions and deformations of Coxeter permutahedra

By Federico Ardila, Federico Castillo, Christopher Eur, Alexander Postnikov. Advances in Mathematics, 2019

53 citations recorded by the source corpus.

We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This family of polytopes contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra, polymatroids, and submodular functions to any finite reflection group.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6cb4c05b27af93116484e11cd2429e6e91b7b976

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Stellahedral geometry of matroids (2022, background): “A standard correspondence between polyhedra and divisors on toric varieties [CLS11, §6.2] (see also [ACEP20, §2.4]) states the following: For a lattice polytope Q and the toric variety 𝑋 𝑄 deﬁned by its normal fan Σ 𝑄 , the base-point-free torus-invariant divisors on 𝑋 𝑄 are in bijection with…”
Simplicial generation of Chow rings of matroids (2019, unknown): “ following specialization of Theorem 2.1.4 to ΣAn was recognized in various works ([Edm70, Mur03, DF10, AA17]); for a modern treatment and generalization to arbitrary Coxeter root systems we point to [ACEP19]. Proposition 2.2.3. The following are equivalent for a divisor D= P ∅(S(E cSxS ∈A 1(Σ An). ”