Department of

Mathematics


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for events the day of Thursday, March 4, 2021.

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Thursday, March 4, 2021

3:00 pm in Zoom,Thursday, March 4, 2021

Uncrowding Algorithm for Hook-Valued Tableaux

Wencin Poh (UC Davis)

Abstract: Whereas set-valued tableaux are the combinatorial objects associated to stable (Grassmann) Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. 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. This uncrowding algorithm intertwines with the crystal operators on hook-valued tableaux. We also provide an alternative uncrowding algorithm that “uncrowds” the entries in the leg instead of the arm of the hooks. As an application, we obtain various expansions of the canonical Grothendieck polynomials.