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Mitosis recursion for coefficients of Schubert polynomials

Ezra Miller
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Abstract

Mitosis is a rule introduced by [Knutson-Miller, 2002] for manipulating subsets of the n by n grid. It provides an algorithm that lists the reduced pipe dreams (also known as rc-graphs) [Fomin-Kirillov, Bergeron-Billey] for a permutation w in S_n by downward induction on weak Bruhat order, thereby generating the coefficients of Schubert polynomials [Lascoux-Schutzenberger] inductively. This note provides a short and purely combinatorial proof of these properties of mitosis.

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Ezra Miller. 2002-12-10. Mitosis recursion for coefficients of Schubert polynomials. https://arxiv.org/abs/math/0212131

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