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Hook-valued Tableaux Uncrowding and Tableau Switching by Jang, Jihyeug; Kim, Jang Soo; Pan, Jianping; Pappe, Joseph; Schilling, Anne is a scholarly article available to read on EtoBox.

What is Hook-valued Tableaux Uncrowding and Tableau Switching about?

Refined canonical stable Grothendieck polynomials were introduced by Hwang, Jang, Kim, Song, and Song. There exist two combinatorial models for these polynomials: one using hook-valued tableaux and the other using pairs of a semistandard Young tableau and (what we call) an exquisite tableau. An uncrowding algorithm on hook-valued tableaux was introduced by Pan, Pappe, Poh, and Schilling. In this paper, we discover a novel connection between the two models via the uncrowding and Goulden--Greene's jeu de taquin algorithms, using a classical result of Benkart, Sottile, and Stroomer on tableau switching. This connection reveals a hidden symmetry of the uncrowding algorithm defined on hook-valued tableaux. As a corollary, we obtain another combinatorial model for the refined canonical stable Grothendieck polynomials in terms of biflagged tableaux, which naturally appear in the characterization of the image of the uncrowding map.

Author

Jang, Jihyeug; Kim, Jang Soo; Pan, Jianping; Pappe, Joseph; Schilling, Anne

Published

2024

Language

EN