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Creators/Authors contains: "Dorpalen-Barry, Galen"

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Equivariant Cohomology and Conditional Oriented Matroids

https://doi.org/10.1093/imrn/rnad025

Dorpalen-Barry, Galen; Proudfoot, Nicholas; Wang, Jidong (May 2024, International Mathematics Research Notices)

Abstract We give a cohomological interpretation of the Heaviside filtration on the Varchenko–Gelfand ring of a pair $$({\mathcal{A}},{\mathcal{K}})$$, where $${\mathcal{A}}$$ is a real hyperplane arrangement and $${\mathcal{K}}$$ is a convex open subset of the ambient vector space. This builds on work of the first author, who studied the filtration from a purely algebraic perspective, as well as work of Moseley, who gave a cohomological interpretation in the special case where $${\mathcal{K}}$$ is the ambient vector space. We also define the Gelfand–Rybnikov ring of a conditional oriented matroid, which simultaneously generalizes the Gelfand–Rybnikov ring of an oriented matroid and the aforementioned Varchenko–Gelfand ring of a pair. We give purely combinatorial presentations of the ring, its associated graded, and its Rees algebra.
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Ian G. Macdonald: Works of Art; Hochschild Polytopes; Toric and Permutoric Promotion; Smirnov Words and the Delta Conjectures; The Poincaré-extended ab-Index; Colored Permutation Statistics by Conjugacy Class; Upho Lattices and Their Cores; Pattern Heights and The Minimal Power of q in a Kazhdan-Lusztig Polynomial; Rowmotion Markov Chains; Enumerating The Faces of Split Matroid Polytopes; From Higher Bruhat Orders to Steenrod Cup-i Coproducts; On The Size of Bruhat Intervals; Vines and MAT-Labeled Graphs; Configuration Spaces and Peak Representations; A determinantal Point Process Approach to Scaling and Local Limits of Random Young Tableaux; Generalized Heawood Graphs and Triangulations of Tori; The Somewhere-To-Below Shuffles in The Symmetric Group and Hecke Algebras; Dyck Combinatorics in p-Kazhdan-Lusztig Theory; A Framework Unifying Some Bijections for Graphs and Its Connection to Lawrence Polytopes; Shi Arrangements and Low Elements in Coxeter Groups; Universal Plücker Coordinates for the Wronski Map and Positivity in Real Schubert Calculus; 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Murnaghan-Type Representations of the Elliptic Hall Algebra; Plane Partitions and Rowmotion on Rectangular and Trapezoidal Posets; Projective Dimension of Weakly Chordal Graphic Arrangements; Realizing the s-Permutahedron via Flow Polytopes; Monomial Expansions for q-Whittaker and Modified Hall-Littlewood Polynomials; Extremal Weight Crystals over Affine Lie Algebras of Infinite Rank; Lascoux Polynomials and Gelfand-Zetlin Patterns; Chain Polynomials of Generalized Paving Matroids; A Galois Structure on The Orbit of Large Steps Walks in The Quadrant; Locally Invariant Vectors in Representations of Symmetric Groups; Excedance quotients, Quasisymmetric Varieties, and Temperley-Lieb algebras; Combinatorial Properties of Triangular Partitions; Asymptotics of Bounded Lecture-Hall Tableaux; Shuffle Theorems and Sandpiles; Real Matroid Schubert Varieties, Zonotopes, and Virtual Weyl Groups; Chromatic Functions, Interval Orders, and Increasing Forests; Crystals for Variations of Decomposition Tableaux; 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Ram, Arun; Macdonald, Ian G; Pilaud, Vincent; Poliakova, Daria; Defant, Colin; Madhukara, Rachana; Thomas, Hugh; Iraci, Alessandro; Nadeau, Philippe; Vanden_Wyngaerd, Anna; et al (September 2024, Séminaire lotharingien de combinatoire)
Gaetz, Christian (Ed.)
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