  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.
