2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65937Mitosis 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.9 pages, to appear in JCTACombinatoricstext