Journal of Integer Sequences, Vol. 17 (2014), Article 14.1.5

Enumeration of Edges in Some Lattices of Paths

Luca Ferrari
Università di Firenze
Dipartimento di Matematica e Informatica "U. Dini"
viale Morgagni 65
50134 Firenze

Emanuele Munarini
Politecnico di Milano
Dipartimento di Matematica
Piazza Leonardo da Vinci 32
20133 Milano


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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(Concerned with sequences A000045 A000108 A000204 A000984 A001006 A001263 A001629 A001850 A002054 A002426 A002457 A006318 A025567 A026002 A027907 A090981 A095977 A108666 A110470 A132894.)

Received January 14 2013; revised versions received October 29 2013; December 9 2013. Published in Journal of Integer Sequences, December 16 2013.

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