Mishna, MarniTrandafir, Stefan2025-03-102025-03-102024Mishna, M. y Trandafir, S. (2024). Estimating and computing Kronecker coefficients: a vector partition function approach. Australasian Journal of Combinatorics, 90 (2), 121-154.1034-49422202-3518https://hdl.handle.net/11441/169826We study the Kronecker coefficients gλ,µ,ν via a formula that was described by Mishna, Rosas and Sundaram (2018), in which the coefficients are expressed as a signed sum of vector partition function evaluations. In particular, we use this formula to determine formulas to evaluate, bound, and estimate gλ,µ,ν in terms of the lengths of the partitions λ, µ and ν. We describe a computational tool to compute Kronecker coefficients gλ,µ,ν with ℓ(µ) ≤ 2, ℓ(ν) ≤ 4, ℓ(λ) ≤ 8. We present a set of new vanishing conditions for the Kronecker coefficients by relating to the vanishing of the related atomic Kronecker coefficients, themselves given by a single vector partition function evaluation. We give a stable face of the Kronecker polyhedron for any positive integers m, n. Finally, we give upper bounds on both the atomic Kronecker coefficients and Kronecker coefficients.application/pdf34 p.engAttribution-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nd/4.0/Kronecker coefficientsVector partition functioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess