Proof of a conjecture of Morales–Pak–Panova on reverse plane partitions

Abstract

Using the equivariant cohomology theory, Naruse obtained a hook length formula for the number of standard Young tableaux of skew shape λ/μ. Morales, Pak and Panova found two q-analogues of Naruse's formula respectively by counting semistandard Young tableaux of shape λ/μ and reverse plane partitions of shape λ/μ. When λ and μ are both staircase shape partitions, Morales, Pak and Panova conjectured that the generating function of reverse plane partitions of shape λ/μ can be expressed as a determinant whose entries are related to q-analogues of the Euler numbers. The objective of this paper is to settle this conjecture.