Séminaire Lotharingien de Combinatoire, 78B.70 (2017), 12 pp.

Emmanuel Briand, Amarpreet Rattan and Mercedes Rosas

On the Growth of Kronecker Coefficients

Abstract. We present a new stability phenomenon for Kronecker coefficients, that we call hook stability: the Kronecker coefficients stabilize if we add cells to the first row and first column of each of the indexing partitions, simultaneously. We also show that when we increase the sizes of the first two rows of their three indexing partitions, in some appropriate way, the Kronecker coefficients grow linearly, and we are able to give asymptotic estimates.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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