Plane partitions and the combinatorics of some families of reduced Kronecker coefficients.

Laura Colmenarejo (1)

1 DALG-US - Departamento de Algebra [Sevilla]

We compute the generating function of some families of reduced Kronecker coefficients. We give a combi- natorial interpretation for these coefficients in terms of plane partitions. This unexpected relation allows us to check that the saturation hypothesis holds for the reduced Kronecker coefficients of our families. We also compute the quasipolynomial that govern these families, specifying the degree and period. Moving to the setting of Kronecker co- efficients, these results imply some observations related to the rate of growth experienced by the families of Kronecker coefficients associated to the reduced Kronecker coefficients already studied.

Domaines: Combinatoire [math.CO]

Laura Colmenarejo. Plane partitions and the combinatorics of some families of reduced Kronecker coefficients.. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6345⟩. ⟨hal-02173387⟩