2024-02-072024-02-072021-04-01Mishna, M., Rosas Celis, M.H. y Sundaram, S. (2021). Vector partition functions and Kronecker coefficients. Journal of Physics A: Mathematical and Theoretical, 54 (20), 205204-1. https://doi.org/10.1088/1751-8121/abf45b.1751-81131751-8121https://hdl.handle.net/11441/154815The Kronecker coefficients are the structure constants for the restriction of irreducible representations of the general linear group GL(nm) into irreducibles for the subgroup GL(n) × GL(m). In this work we study the quasipolynomial nature of the Kronecker function using elementary tools from polyhedral geometry.We write the Kronecker function in terms of coefficients of a vector partition function. This allows us to define a new family of coefficients, the atomic Kronecker coefficients. Our derivation is explicit and self-contained, and gives a new exact formula and an upper bound for the Kronecker coefficients in the first nontrivial case.application/pdf30 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Kronecker coefficientsvector partition functionssubgroup restriction probleminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1088/1751-8121/abf45b