MCS Seminar: Mohamed Omar. Peak Polynomials

10 March 2017 (Fri), 18:00-19:00
At Lecture Theatre 1, Saga

Abstract: A permutation of the set {1, 2, …, n} is a rearrangement of it. In a given permutation, an element is a peak if it is larger than the numbers next to it. For instance, the permutation 1432 has a peak (only) in the second position. This talk investigates the question: How many permutations of {1, 2, …, n} have peaks at a prescribed set of positions? We introduce this notion and discuss the resolution of an open problem of Billey, Burdzy and Sagan. This is joint work with Alex Diaz-Lopez, Pamela Harris and Erik Insko.