Theory of Representations, Algebra, Combinatorics
Breaking down the reduced Kronecker coefficients
Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 463-468.

We resolve three interrelated problems on reduced Kronecker coefficients $\overline{g}\left(\alpha ,\beta ,\gamma \right)$. First, we disprove the saturation property which states that $\overline{g}\left(N\alpha ,N\beta ,N\gamma \right)>0$ implies $\overline{g}\left(\alpha ,\beta ,\gamma \right)>0$ for all $N>1$. Second, we esimate the maximal $\overline{g}\left(\alpha ,\beta ,\gamma \right)$, over all $|\alpha |+|\beta |+|\gamma |=n$. Finally, we show that computing $\overline{g}\left(\lambda ,\mu ,\nu \right)$ is strongly $\mathrm{#P}$-hard, i.e. $\mathrm{#P}$-hard when the input $\left(\lambda ,\mu ,\nu \right)$ is in unary.

Accepted:
Revised after acceptance:
Published online:
DOI: 10.5802/crmath.60
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
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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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