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).
Enumeration of edges in some lattices of paths / Luca Ferrari; Emanuele Munarini. - In: JOURNAL OF INTEGER SEQUENCES. - ISSN 1530-7638. - ELETTRONICO. - 17:(2014), pp. 0-0.
Enumeration of edges in some lattices of paths
FERRARI, LUCA;
2014
Abstract
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).
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