Hook formulas for skew shapes

Alejandro H. Morales (1) , Igor Pak (1) , Greta Panova (2)

1 UCLA - University of California [Los Angeles]
2 University of Pennsylvania

The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We give two q-analogues of Naruse's formula for the skew Schur functions and for counting reverse plane partitions of skew shapes. We also apply our results to border strip shapes and their generalizations.

Mots clés: Combinatorics

Domaines: Combinatoire [math.CO]

Alejandro H. Morales, Igor Pak, Greta Panova. Hook formulas for skew shapes. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6354⟩. ⟨hal-02166348⟩