Mixed jeu de taquin and a problem of Soojin Cho
Abstract
Serrano (2010) introduced the shifted plactic monoid, governing Haiman's (1989) mixed insertion algorithm, as a type B analogue of the classical plactic monoid that connects jeu de taquin of Young tableaux with the Robinson-Schensted-Knuth insertion algorithm. Serrano proposed a corresponding definition of skew shifted plactic Schur functions. Cho (2013) disproved Serrano's conjecture regarding this definition, by showing that the functions do not live in the desired ring and hence cannot provide an algebraic interpretation of tableau rectification or of the corresponding structure coefficients. Cho asked for a new definition with particular properties. We introduce such a definition and prove that it behaves as desired. We also introduce a new jeu de taquin theory that computes mixed insertion.
Keywords
Cite
@article{arxiv.2602.18632,
title = {Mixed jeu de taquin and a problem of Soojin Cho},
author = {Santiago Estupiñán-Salamanca and Oliver Pechenik},
journal= {arXiv preprint arXiv:2602.18632},
year = {2026}
}
Comments
18 pages. Fixed a cleveref version bug