Combinatorics Seminar: "Peaks and descents of permutations: A story with open questions"

Abstract: Peaks and descents of permutations are properties based on when a permutation has the consecutive patterns 132 or 231 for peaks and 21 for descents. They have been studied algebraically for some time (e.g. Solomon algebra, peak algebra) and more recently, from a combinatorial point of view. In this talk, I will give an overview of some important facts about them with open questions intertwined. While the talk will focus on permutations, some results will be mentioned about signed permutations (type B/C Coxeter groups) and even signed permutations (type D Coxeter group).

Host: Martha Precup