Tres lecciones en combinatoria algebraica. I. Matrices totalmente no negativas y funciones sim\'etricas

TL;DR

This paper introduces totally non-negative matrices and explores their connection to symmetric functions within the broader context of algebraic and geometric combinatorics, setting the stage for further research.

Contribution

It provides an introductory overview of totally non-negative matrices and their relation to symmetric functions, highlighting open problems in algebraic and geometric combinatorics.

Findings

Overview of totally non-negative matrices

Connection between matrices and symmetric functions

Identification of open problems in the field

Abstract

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 primera parte presenta una introduccion a las matrices totalmente no negativas, y su relacion con las funciones simetricas. 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 presents an introduction to totally non-negative matrices and their relationship with symmetric functions.