Séminaire Lotharingien de Combinatoire, 95B.83 (2026), 12 pp.
Avery St. Dizier, Linus Setiabrata and Tianyi Yu
Generalized Orthodontia, Punched Tableaux, and Lascoux Expansion of Sheared Characters
Abstract.
We introduce double inhomogeneous
analogues GD(x,y) of characters of
flagged Schur modules based on Magyar's orthodontia formula for
diagrams, giving a new formula for double Grothendieck
polynomials. The polynomials GD refine sheared
characters. Using Lascoux's theory of punched tableaux,
we establish an inhomogeneous extension of Reiner-Shimozono's result
that multiplication by x1 ... xk
preserves key positivity, and prove that the
reverse-complement RD(m,n)(x)
of a sheared character expands positively in the basis of Lascoux polynomials.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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