Breaking down the reduced Kronecker coefficients

2020/03/25 by Igor Pak, Greta Panova, Pak, Igor +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2003.11398

openalex publication_date 2020/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We resolve three interrelated problems on reduced Kronecker coefficients g(α,β,γ). First, we disprove the saturation property which states that g(Nα,Nβ,Nγ)>0 implies g(α,β,γ)>0 for all N>1. Second, we esimate the maximal g(α,β,γ), over all |α|+|β|+|γ| = n. Finally, we show that computing g(λ,μ,ν) is strongly # P-hard, i.e. #P-hard when the input (λ,μ,ν) is in unary.

Citations

• Upper bounds on Kronecker coefficients with few rows

Related

• On the complexity of computing Kronecker coefficients
• Combinatorics on a family of reduced Kronecker coefficients
• Estimating and computing Kronecker Coefficients: a vector partition function approach
• Combinatorics on several families of Kronecker coefficients related to plane partitions
• Upper bounds on Kronecker coefficients with few rows