RSK linear operators and the Vershik-Kerov-Logan-Shepp curve
Combinatorics
2025-04-09 v1
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.
Keywords
Cite
@article{arxiv.2504.05510,
title = {RSK linear operators and the Vershik-Kerov-Logan-Shepp curve},
author = {Duy Phan and David Xia},
journal= {arXiv preprint arXiv:2504.05510},
year = {2025}
}
Comments
12 pages