Uncrowding algorithm for hook-valued tableaux
Abstract
Whereas set-valued tableaux are the combinatorial objects associated to stable Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. In this paper, we define a novel uncrowding algorithm for hook-valued tableaux. The algorithm "uncrowds" the entries in the arm of the hooks and yields a set-valued tableau and a column-flagged increasing tableau. We prove that our uncrowding algorithm intertwines with crystal operators. An alternative uncrowding algorithm that "uncrowds" the entries in the leg instead of the arm of the hooks is also given. As an application of uncrowding, we obtain various expansions of the canonical Grothendieck polynomials.
Cite
@article{arxiv.2012.14975,
title = {Uncrowding algorithm for hook-valued tableaux},
author = {Jianping Pan and Joseph Pappe and Wencin Poh and Anne Schilling},
journal= {arXiv preprint arXiv:2012.14975},
year = {2025}
}
Comments
Corrected typo in Definition 3.33 line 5: "column" should be "row"