Work

RSK Linear Operators and the Vershik-Kerov-Logan-Shepp Curve

Year: 2026

Type: article

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.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/14670

Authors: Duy Phan, David Xia

Institution: University of Illinois Urbana-Champaign

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, University of Illinois at Urbana-Champaign

Award: RTG: Research in Combinatorics