2021/04/28 by Florian Aigner, Aigner, Florian, Gabriel Frieden +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2104.13846
openalex publication_date 2021/04/28 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28
We present a probabilistic generalization of the Robinson--Schensted correspondence in which a permutation maps to several different pairs of standard Young tableaux with nonzero probability. The probabilities depend on two parameters q and t, and the correspondence gives a new proof of the squarefree part of the Cauchy identity for Macdonald polynomials. By specializing q and t in various ways, one recovers both the row and column insertion versions of the Robinson--Schensted correspondence, as well as several q- and t-deformations of row and column insertion which have been introduced in recent years in connection with integrable probability.