Breaking down the reduced Kronecker coefficients

Igor Pak; Greta Panova

doi:10.5802/crmath.60

Théorie des représentations, Algèbre, Combinatoire

Breaking down the reduced Kronecker coefficients
[Analyse fine des coefficients de Kronecker réduits]

Igor Pak ¹ ; Greta Panova ²

¹ Department of Mathematics, UCLA, Los Angeles, CA 90095, USA
² Department of Mathematics, USC, Los Angeles, CA 90089, USA

Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 463-468.

Résumé

We resolve three interrelated problems on reduced Kronecker coefficients $\bar{g} (α, β, γ)$ . First, we disprove the saturation property which states that $\bar{g} (N α, N β, N γ) > 0$ implies $\bar{g} (α, β, γ) > 0$ for all $N > 1$ . Second, we esimate the maximal $\bar{g} (α, β, γ)$ , over all $| α | + | β | + | γ | = n$ . Finally, we show that computing $\bar{g} (λ, μ, ν)$ 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 : 10.5802/crmath.60

Affiliations des auteurs :

Igor Pak ¹ ; Greta Panova ²

¹ Department of Mathematics, UCLA, Los Angeles, CA 90095, USA
² Department of Mathematics, USC, Los Angeles, CA 90089, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@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},
     pages = {463--468},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {4},
     year = {2020},
     doi = {10.5802/crmath.60},
     language = {en},
}

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Igor Pak; Greta Panova. Breaking down the reduced Kronecker coefficients. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 463-468. doi : 10.5802/crmath.60. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.60/

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