Jang Soo Kim ; Karola Mészáros ; Greta Panova ; David B. Wilson - Dyck tilings, linear extensions, descents, and inversions

dmtcs:3081 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3081
Dyck tilings, linear extensions, descents, and inversions

Authors: Jang Soo Kim 1; Karola Mészáros 2; Greta Panova 3; David B. Wilson 4

  • 1 University of Minnesota [Twin Cities]
  • 2 Department of Mathematics [Ann Arbor]
  • 3 University of California [Los Angeles]
  • 4 Microsoft Research [Redmond]

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: Dyck path, linear extension, tree poset, perfect matching,Dyck tiling,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Linked publications - datasets - softwares

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
  • 10.46298/dmtcs.2891
  • 10.46298/dmtcs.2891
  • 10.37236/3440
  • 10.37236/3440
  • 1109.0371
  • 10.48550/arxiv.1109.0371
Tree-like tableaux

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