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arXiv · 1702.00132

Multiplication of a Schubert polynomial by a Stanley symmetric polynomial

Sami Assaf
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Abstract

We prove, combinatorially, that the product of a Schubert polynomial by a Stanley symmetric polynomial is a truncated Schubert polynomial. Using Monk's rule, we derive a nonnegative combinatorial formula for the Schubert polynomial expansion of a truncated Schubert polynomial. Combining these results, we give a nonnegative combinatorial rule for the product of a Schubert and a Schur polynomial in the Schubert basis.

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Sami Assaf. 2017-02-01. Multiplication of a Schubert polynomial by a Stanley symmetric polynomial. https://arxiv.org/abs/1702.00132

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