Discrete Math Seminar: Alejandro Morales

The celebrated hook-length formula of Frame, Robinson and Thrall from 1954 gives a product formula for the number of standard Young tableaux of straight shape. No such product formula exists for the number of standard Young tableaux of skew shapes. In 2014, Naruse announced a formula for skew shapes as a positive sum of products of hook-lengths proved using equivariant cohomology and excited diagrams of Ikeda-Naruse and Kreiman. We prove Naruse's formula combinatorially and we give two q-analogues of this formula involving semistandard Young tableaux and reverse plane partitions of skew shape. The first q-analogue is proved algebraically. We show that the restricted Hillman-Grassl correspondence is a bijection explaining these q-analogues. Joint work with Igor Pak and Greta Panova.