The Haglund–Remmel–Wilson identity for set partitions

Abstract

In 2015, Remmel and Wilson proved the following conjecture of Jim Haglund for permutations∑π∈Snqinv(π)∏j∈Des(π)(1+zq1+inv□,j(π))=∑π∈Snqmaj(π)∏j=1des(π)(1+zqj). Wilson extended this identity to words in 2016. In this note, we prove that this identity holds for set partitions.