Related papers: Minuscule Coxeter Dressians

Motivated by the desire to understand the geometry of the basic loci in the reduction of Shimura varieties, we study their "group-theoretic models" -- generalized affine Deligne-Lusztig varieties -- in cases where they have a particularly…

We compute the characteristic polynomials of affine Cartan, adjacency matrices and Coxeter polynomials of the associated Coxeter system using Chebyshev polynomials. We give explicit factorization of these polynomials as products of…

We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks where the $i$-morphisms are given by $i$-fold coisotropic correspondences.…

We study the subvariety of singular sections, the discriminant, of a base point free linear system $|L|$ on a smooth toric variety $X$. On one hand we describe pairs $(X,L)$ for which the discriminant is of low dimension. Precisely, we…

This paper is devoted to the study of equidistributional properties of \textit{totient points} in $\mathbb{N}^r$, that is, of coprime $r$-tuples of integers, with particular emphasis on some relevant sets of totient points fulfilling extra…

Kamiya, Takemura, and Terao introduced a characteristic quasi-polynomial which enumerates the numbers of elements in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic…

Let X be a space of constant curvature and P be a convex polyhedron in X. A Coxeter decomposition of the polyhedron P is a decomposition of P into finitely many Coxeter polyhedra, such that any two polyhedra having a common facet are…

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…

We introduce a notion of tropical vector bundle on a tropical toric variety which is a tropical analogue of a torus equivariant vector bundle on a toric variety. Alternatively it can be called a toric matroid bundle. We define equivariant…

Ehrhart theory measures a polytope P discretely by counting the lattice points inside its dilates P, 2P, 3P, .... We compute the Ehrhart quasipolynomials of the standard Coxeter permutahedra for the classical Coxeter groups, expressing them…

Each Gr\"obner stratum of a tropical variety is a connected set of points, all of which induce the same initial subscheme. The Gr\"obner stratification is a coarsening of the decomposition into Gr\"obner polyhedra, and has the advantage…

In this paper, we present a lattice-theoretic characterization for valuated matroids, which is an extension of the well-known cryptomorphic equivalence between matroids and geometric lattices ($=$ atomistic semimodular lattices). We…

We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating…

We provide a weaker version of the generalized lifting property which holds in complete generality for all finite Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We…

We study the modular representations of finite groups of Lie type arising in the cohomology of certain quotients of Deligne-Lusztig varieties associated with Coxeter elements. These quotients are related to Gelfand-Graev representations and…

We describe the ideals, especially the prime ideals, of semirings of polynomials over layered domains, and in particular over supertropical domains. Since there are so many of them, special attention is paid to the ideals arising from…

Let $X$ be a smooth irreducible quasi-projective algebraic variety over a number field $K$. Suppose $X$ is equipped with a $p$-adic \'{e}tale local system compatible with an admissible graded-polarized variation of mixed Hodge structures on…

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary…

In this paper we introduce valuated $\Delta$-matroids, a natural generalization of two objects of study in matroid theory: valuated matroids and $\Delta$-matroids. We show that these objects exhibit nice properties analogous to ordinary…

We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by A. Berget, C. Eur, H. Spink and D. Tseng to the product space…