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arXiv · 2504.05510

RSK linear operators and the Vershik-Kerov-Logan-Shepp curve

Duy Phan·David Xia
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Abstract

Stelzer and Yong (2024) studied the Robinson-Schensted-Knuth (RSK) correspondence as a linear operator on the coordinate ring of matrices. They showed that this operator is block diagonal and conjectured that, in a special block, most diagonal entries vanish. We establish this conjecture by identifying these zeros with certain Schensted insertion interactions and analyzing them probabilistically using the Vershik-Kerov-Logan-Shepp Limit Shape Theorem.

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Duy Phan, David Xia. 2025-04-07. RSK linear operators and the Vershik-Kerov-Logan-Shepp curve. https://arxiv.org/abs/2504.05510

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