Geodesic
Maximal 0-1-fillings of moon polyominoes with restricted chain lengths and rc-graphs
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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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. 
@article{DMTCS_2011_special_260_a70,
     author = {Rubey, Martin},
     title = {Maximal 0-1-fillings of moon polyominoes with restricted chain lengths and rc-graphs},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2957},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2957/}
}
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%V DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
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Rubey, Martin. Maximal 0-1-fillings of moon polyominoes with restricted chain lengths and rc-graphs. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2957. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2957/

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