Tres lecciones en combinatoria algebraica. III. Arreglos de hiperplanos

TL;DR

This paper introduces hyperplane arrangements within algebraic and geometric combinatorics, discussing key results and open problems in the field, aimed at providing a comprehensive overview for researchers.

Contribution

It offers a detailed combinatorial introduction to hyperplane arrangements, connecting them with broader algebraic and geometric combinatorics topics.

Findings

Overview of hyperplane arrangements and their combinatorial properties

Discussion of open problems in hyperplane arrangements

Connections with totally non-negative matrices and symmetric group representations

Abstract

In this series of three articles, we give an exposition of various results and open problems in three areas of algebraic and geometric combinatorics: totally non-negative matrices, representations of the symmetric group, and hyperplane arrangements. This first part is an introduction to hyperplane arrangements from a combinatorial point of view. ----- En esta serie de tres articulos, damos una exposicion de varios resultados y problemas abiertos en tres areas de la combinatoria algebraica y geometrica: las matrices totalmente no negativas, las representaciones del grupo simetrico, y los arreglos de hiperplanos. Esta tercera parte presenta una introduccion a los arreglos de hiperplanos desde un punto de vista combinatorio.