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Dyck tilings, linear extensions, descents, and inversions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012) Cet article a éte moissonné depuis la source Episciences

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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. 
@article{DMTCS_2012_special_263_a67,
     author = {Kim, Jang Soo and M\'esz\'aros, Karola and Panova, Greta and Wilson, David B.},
     title = {Dyck tilings, linear extensions, descents, and inversions},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2012},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     doi = {10.46298/dmtcs.3081},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3081/}
}
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AU  - Panova, Greta
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%A Panova, Greta
%A Wilson, David B.
%T Dyck tilings, linear extensions, descents, and inversions
%J Discrete mathematics & theoretical computer science
%D 2012
%V DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
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Kim, Jang Soo; Mészáros, Karola; Panova, Greta; Wilson, David B. Dyck tilings, linear extensions, descents, and inversions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi: 10.46298/dmtcs.3081

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