D’Adderio, Michele Moci, Luca
Published in
Advances in Mathematics

We introduce the notion of an arithmetic matroid whose main example is a list of elements of a finitely generated abelian group. In particular, we study the representability of its dual, providing an extension of the Gale duality to this setting. Guided by the geometry of generalized toric arrangements, we provide a combinatorial interpretation of ...

d'Antonio, Giacomo Delucchi, Emanuele

We prove that the complement of a complexified toric arrangement has the homotopy type of a minimal CW-complex, and thus its homology is torsion-free. To this end, we consider the toric Salvetti complex, a combinatorial model for the arrangement's complement. Using diagrams of acyclic categories we obtain a stratification of this combinatorial mode...

Ardila, Federico Castillo, Federico Henley, Michael

Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its *arithmetic* Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems $A_n, B_n, C_n$, and $D_n$ with resp...

Ehrenborg, Richard Readdy, Margaret
Published in
Journal of Combinatorial Theory, Series A

We determine the cd-index of the induced subdivision arising from a manifold arrangement. This generalizes earlier results in several directions: (i) One can work with manifolds other than the n-sphere and n-torus, (ii) the induced subdivision is a Whitney stratification, and (iii) the submanifolds in the arrangement are no longer required to be of...

Chandrasekhar, Karthik Deshpande, Priyavrat
Published in
Indian Journal of Pure and Applied Mathematics

A toric arrangement is a finite collection of codimension-1 subtori in a torus. These subtori stratify the ambient torus into faces of various dimensions. Let fi denote the number of i-dimensional faces; these so-called face numbers satisfy the Euler relation ∑i(-1)ifi = 0. However, not all tuples of natural numbers satisfying this relation arise a...

Bergvall, Olof
Published in
Research in the Mathematical Sciences

We develop an algorithm for computing the cohomology of complements of toric arrangements. In the case a finite group Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\...