Maximal 0–1-fillings of moon polyominoes with restricted chain lengths and rc-graphs |
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Authors: | Martin Rubey |
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Institution: | Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany |
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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. |
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Keywords: | primary 05A19 secondary 05E05 06A07 |
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