Coxeter submodular functions and deformations of Coxeter permutahedra

DOI10.1016/j.aim.2020.107039zbMath1435.05234arXiv1904.11029OpenAlexW3005921796MaRDI QIDQ2308296

Alexander Postnikov, Federico Ardila, Federico Castillo, Christopher Eur

Publication date: 2 April 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.11029

zbMATH Keywords

submodular functionCoxeter groupCoxeter matroidgeneralized permutahedronpolymatroidnef cone

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Combinatorial aspects of matroids and geometric lattices (05B35) Combinatorial geometries and geometric closure systems (51D20) Combinatorial aspects of algebraic geometry (05E14)

Related Items

Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity, Hopf Monoids and Generalized Permutahedra, Stellahedral geometry of matroids, Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors, Minkowski summands of cubes, Subdivisions of generalized permutahedra, Tautological classes of matroids, The geometry of geometries: matroid theory, old and new, Polypositroids, An effective solution to convex 1-body \(N\)-representability, Deformation cones of hypergraphic polytopes, Signed permutohedra, delta‐matroids, and beyond, Removahedral congruences versus permutree congruences, Tropical flag varieties, Minkowski summands of cubes, The polytope algebra of generalized permutahedra, The polytope algebra of generalized permutahedra, The universal valuation of Coxeter matroids, Pruned inside-out polytopes, combinatorial reciprocity theorems and generalized permutahedra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Core-based criterion for extreme supermodular functions
• Mixed volumes of hypersimplices
• Permutahedra and generalized associahedra.
• \(K\)-classes for matroids and equivariant localization
• Constructions and complexity of secondary polytopes
• Descent systems for Bruhat posets
• Bruhat interval polytopes
• Wythoff's construction for Coxeter groups
• Faces of generalized permutohedra
• Matroid polytopes and their volumes
• Triangulations. Structures for algorithms and applications
• Cambrian fans.
• Combinatorial geometries, convex polyhedra, and Schubert cells
• Signed graph coloring
• Buildings of spherical type and finite BN-pairs
• Discrete convex analysis
• Equivariant cohomology, Koszul duality, and the localization theorem
• The asymptotic number of geometries
• Coxeter matroids. With illustrations by Anna Borovik
• Polytopal realizations of finite type \(\mathbf{g}\)-vector fans
• Combinatorial optimization. Polyhedra and efficiency (3 volumes)
• Realization of the Stasheff polytope
• On the asymptotic proportion of connected matroids
• Compatibility fans for graphical nested complexes
• Coxeter cones and their \(h\)-vectors
• Cambrian lattices.
• Submodular functions and optimization.
• Standard parabolic subsets of highest weight modules
• Buildings
• Convex Rank Tests and Semigraphoids
• Permutohedra, Associahedra, and Beyond
• Quotients of Coxeter complexes and 𝑃-partitions
• Semimodular Functions and Combinatorial Geometries
• On the self-linking of knots
• Deformation Cones of Nested Braid Fans
• Decomposable convex polyhedra
• Inverses of Cartan matrices of Lie algebras and Lie superalgebras