Mingjia Yang, Rutgers University

Abstract

A pattern is a list a = [a1, a2, . . . , ar] (r ≥ 1) of non-negative integers. We say a partition λ = (λ1, . . . , λk) contains the pattern a = [a1, a2, . . . , ar] if there exists 1 ≤ i ≤ k − r such that λi − λi+1 = a1, λi+1 − λi+2 = a2, . . . , λi+r−1 − λi+r = ar. We present a systematic way to efficiently count partitions that avoid patterns either globally, or according to some congruence conditions, along with initial conditions. Using this approach, we are currently searching for new partition identities and have already found some. These identities will be presented as well as future work directions. This is joint work with Matthew C. Russell and Doron Zeilberger.