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Comptes Rendus. Mathématique
Théorie des représentations, Algèbre, Combinatoire
Breaking down the reduced Kronecker coefficients
[Analyse fine des coefficients de Kronecker réduits]
Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 463-468.

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.

Reçu le : 2020-04-06
Accepté le : 2020-04-25
Accepté après révision le : 2020-05-03
Publié le : 2020-07-28
DOI : https://doi.org/10.5802/crmath.60
@article{CRMATH_2020__358_4_463_0,
     author = {Igor Pak and Greta Panova},
     title = {Breaking down the reduced Kronecker coefficients},
     journal = {Comptes Rendus. Math\'ematique},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {4},
     year = {2020},
     pages = {463-468},
     doi = {10.5802/crmath.60},
     language = {en},
     url = {comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_4_463_0/}
}
Igor Pak; Greta Panova. Breaking down the reduced Kronecker coefficients. Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 463-468. doi : 10.5802/crmath.60. https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_4_463_0/

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