Combinatorics Seminar-Unbalanced Wilf-equivalence

Speaker: Alex Burstein, Howard University
Date and time: Wednesday, September 20, 4-5pm
Place: Rome 771
Title: Unbalanced Wilf-equivalence

Abstract: A pattern is an equivalence class of permtutaions over a totally ordered alphabet under an order isomorphism. A permutation S avoids a pattern P if it has no subsequence order-isomorphic to P. Two sets of patterns, T_1 and T_2, are Wilf-equivalent if, for each n, they are avoided by same number of permutations of length n. A Wilf-equivalence of sets of patterns T_1 and T_2 is balanced if, for each k, T_1 and T_2 contain the same number of patterns of size k. We will consider some of the smallest cases of unbalanced Wilf-equivalence, and their generalizations to infinite families of unbalanced Wilf-equivalences, as well as some conjectured Wilf-equivalences that are still open problems.