Combinatorics Seminar: Combinatorial Proofs of Identities involving Noncommutative Kostka Matrices

Abstract: The noncommutative Kostka matrix K is the transition matrix from the complete homogeneous noncommutative symmetric functions to the immaculate noncommutative symmetric functions. A combinatorial interpretation of its inverse K^-1 was given by Allen and Mason (2023) in terms of tunnel hook coverings. In this talk, we show how to prove matrix identities involving K and K^-1 combinatorially through sign-reversing involutions. We further show how these involutions relate to the work of Eğecioğlu and Remmel (1990) and Sagan and Lee (2006) in the symmetric case involving special rim hook tableaux.

Host: Martha Precup