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arXiv · 2306.04734

Machine-Learning Kronecker Coefficients

Kyu-Hwan Lee
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Abstract

The Kronecker coefficients are the decomposition multiplicities of the tensor product of two irreducible representations of the symmetric group. Unlike the Littlewood--Richardson coefficients, which are the analogues for the general linear group, there is no known combinatorial description of the Kronecker coefficients, and it is an NP-hard problem to decide whether a given Kronecker coefficient is zero or not. In this paper, we show that standard machine-learning algorithms such as Nearest Neighbors, Convolutional Neural Networks and Gradient Boosting Decision Trees may be trained to predict whether a given Kronecker coefficient is zero or not. Our results show that a trained machine can efficiently perform this binary classification with high accuracy ($\approx 0.98$).

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BibTeXRIS

Kyu-Hwan Lee. 2023-06-07. Machine-Learning Kronecker Coefficients. https://arxiv.org/abs/2306.04734

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