The Catalan numbers play a prominent role in combinatorics. Stanley’s book on enumerative combinatorics [1] lists over 95 collections of objects counted by the Catalan numbers. One of the collections of objects counted by the Catalan numbers is the set of Dyck paths of order n. Associated with Dyck paths are the area and bounce score statistics, which lead to the Garsia-Haiman q,t-Catalan sequence.

Loehr gives two new combinatorial interpretations of the Garsia-Haiman q,t-Catalan sequence, involving two particular collections of permutations. A nice feature is that the paper ends with the motivation for finding these new combinatorial interpretations, and also explains the open related problems on the Garsia-Haiman q,t-Catalan sequence.