Abstract
In this paper, we provide explicit formula for the dual Schubert polynomials of a special class of permutations using certain involution principals on RC-graphs, resolving a conjecture by Postnikov and Stanley.
Highlights
Introduction and PreliminariesAlexander Postnikov and Richard Stanley [8] defined dual Schubert Polynomials Dw where the label w belongs to some Weyl group
In type A, the polynomials Dw are dual to the Schubert polynomials Sw with respect to some natural pairing on polynomials
We resolve Conjecture 16.1 of [8], which asks for a form for the dual Schubert polynomial Dw where w is special
Summary
Introduction and PreliminariesAlexander Postnikov and Richard Stanley [8] defined dual Schubert Polynomials Dw where the label w belongs to some Weyl group. Let Dw(x) := Did,w be the dual Schubert polynomial labeled by w ∈ Sn. The polynomials Du,w are defined naturally in a more general context for arbitrary Weyl groups by Postnikov and Stanley [8]. Let RC(w) be the set of all RC-graphs for permutation w.
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