Abstract
We show that maximal 0–1-fillings of moon polynomials with restricted chain lengths can be identified with certain rc-graphs, also known as pipe dreams. In particular, this exhibits a connection between maximal 0–1-fillings of Ferrers shapes and Schubert polynomials. Moreover, it entails a bijective proof showing that the number of maximal fillings of a stack polyomino S with no north-east chains longer than k depends only on k and the multiset of column heights of S. Our main contribution is a slightly stronger theorem, which in turn leads us to conjecture that the poset of rc-graphs with covering relation given by generalised chute moves is in fact a lattice.
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