Mitosis recursion for coefficients of Schubert polynomials
Combinatorics
2007-05-23 v1
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.
Cite
@article{arxiv.math/0212131,
title = {Mitosis recursion for coefficients of Schubert polynomials},
author = {Ezra Miller},
journal= {arXiv preprint arXiv:math/0212131},
year = {2007}
}
Comments
9 pages, to appear in JCTA