A new partial order is defined on the set of Dyck paths of a given length. This partial order is proved to be a meet-semilattice. Its intervals are enumerated and a specific interval is connected with an existing polytope coming from algebraic topology.
Revised:
Accepted:
Published online:
Classification: 05E, 05A15, 05A19, 06A07, 52B
Keywords: Dyck path, semilattice, enumerative combinatorics, interval, Hochschild polytope
@article{ALCO_2020__3_2_433_0, author = {Chapoton, Fr\'ed\'eric}, title = {Some properties of a new partial order on~Dyck paths}, journal = {Algebraic Combinatorics}, pages = {433--463}, publisher = {MathOA foundation}, volume = {3}, number = {2}, year = {2020}, doi = {10.5802/alco.98}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.98/} }
Chapoton, Frédéric. Some properties of a new partial order on Dyck paths. Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 433-463. doi : 10.5802/alco.98. https://alco.centre-mersenne.org/articles/10.5802/alco.98/
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