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.

26 pages with improved exposition. Viewing in color is recommended

References in corpus (1)

• Multiplication of a Schubert polynomial by a Stanley symmetric polynomial

Cited by in corpus (5)

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• Bumpless pipe dreams meet Puzzles