Geodesic
Enumeration of edges in some lattices of paths
Journal of integer sequences, Tome 17 (2014) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We enumerate the edges in the Hasse diagram of several lattices arising in the combinatorial context of lattice paths. Specifically, we consider the case of Dyck, Grand Dyck, Motzkin, Grand Motzkin, Schröder and Grand Schröder lattices. Finally, we give a general formula for the number of edges in an arbitrary Young lattice (which can be interpreted in a natural way as a lattice of paths).
Classification : 05A15, 05A05, 06A07, 06D05
Keywords: (Grand) Dyck path, (Grand) Motzkin path, (Grand) Schröder path, Young lattice, (Grand) Fibonacci poset, formal series, enumeration 
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     author = {Ferrari, Luca and Munarini, Emanuele},
     title = {Enumeration of edges in some lattices of paths},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_1_a6/}
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Ferrari, Luca; Munarini, Emanuele. Enumeration of edges in some lattices of paths. Journal of integer sequences, Tome 17 (2014) no. 1. http://geodesic.mathdoc.fr/item/JIS_2014__17_1_a6/