Dyck tilings, increasing trees, descents, and inversions

@article{Kim2014DyckTI,
  title={Dyck tilings, increasing trees, descents, and inversions},
  author={J. Kim and K. M{\'e}sz{\'a}ros and G. Panova and D. Wilson},
  journal={J. Comb. Theory, Ser. A},
  year={2014},
  volume={122},
  pages={9-27}
}
Cover-inclusive Dyck tilings are tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths, in which tiles are no larger than the tiles they cover. These tilings arise in the study of certain statistical physics models and also Kazhdan-Lusztig polynomials. 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… Expand
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