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Title: Schubert Products for Permutations with Separated Descents
Abstract

We say that two permutations $\pi $ and $\rho $ have separated descents at position $k$ if $\pi $ has no descents before position $k$ and $\rho $ has no descents after position $k$. We give a counting formula, in terms of reduced word tableaux, for computing the structure constants of products of Schubert polynomials indexed by permutations with separated descents, and recognize that these structure constants are certain Edelman–Greene coefficients. Our approach uses generalizations of Schützenberger’s jeu de taquin algorithm and the Edelman–Greene correspondence via bumpless pipe dreams.

 
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NSF-PAR ID:
10379302
Author(s) / Creator(s):
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
International Mathematics Research Notices
Volume:
2023
Issue:
20
ISSN:
1073-7928
Format(s):
Medium: X Size: p. 17461-17493
Size(s):
["p. 17461-17493"]
Sponsoring Org:
National Science Foundation
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