Collaboration on Problems in Algebraic Combinatorics

Collaboration on Problems in Algebraic Combinatorics Collaboration on Problems in Algebraic Combinatorics In 2007, after nine years in industry, I returned to academia. I restarted by working on problems in Catalan combinatorics, among other areas, and Catalan combinatorics continues to fascinate me. The first section of this document describes questions on the Shi arrangement, the sub-area Ive studied over the past few years. In 2014-15, I spent my first sabbatical at University of Talca in Chile, where I worked primarily with Luc Lapointe and Stephen Griffeth. The next two sections are about my work with them. After a 2017 Women in Algebraic Combinatorics meeting in Banff, I started working on problems related to reduced decompositions of permutations and properties of the weak order on the symmetric group. The last section discusses this work. None of the work described here would have been possible without Simons Grant 359602.