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Mitosis recursion for coefficients of Schubert polynomials

2003; Elsevier BV; Volume: 103; Issue: 2 Linguagem: Inglês

10.1016/s0097-3165(03)00020-7

1096-0899

Ezra Miller,

Mathematical Dynamics and Fractals

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