ALGEBRAIC COMBINATORICS

no. 2

Some properties of a new partial order on Dyck paths
Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 433-463.

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.

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Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.98
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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