![]() |
Discrete Mathematics & Theoretical Computer Science |
Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths. We give two bijections between "cover-inclusive'' Dyck tilings and linear extensions of tree posets. The first bijection maps the statistic (area + tiles)/2 to inversions of the linear extension, and the second bijection maps the "discrepancy'' between the upper and lower boundary of the tiling to descents of the linear extension.
Source : ScholeXplorer
IsRelatedTo ARXIV 1109.0371 Source : ScholeXplorer IsRelatedTo DOI 10.37236/3440 Source : ScholeXplorer IsRelatedTo DOI 10.46298/dmtcs.2891 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1109.0371
|