Combinatorics of certain higher $q,t$-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula

Kyungyong Lee, Li Li, Nicholas A. Loehr

The higher $q,t$-Catalan polynomial $C_n^{(m)}(q,t)$ can be defined combinatorially as a weighted sum of lattice paths contained in certain triangles, or algebraically as a complic…