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.

Corrected typo in Definition 3.33 line 5: "column" should be "row"

References in corpus (5)

• Duality and deformations of stable Grothendieck polynomials
• Crystal structures for canonical Grothendieck functions
• Crystal structures for symmetric Grothendieck polynomials
• A crystal on decreasing factorizations in the $0$-Hecke monoid
• Combinatorial relations on skew Schur and skew stable Grothendieck polynomials

Cited by in corpus (1)

• Integrable systems and crystals for edge labeled tableaux