Enumeration of Edges in Some Lattices of Paths
Università di Firenze
Dipartimento di Matematica e Informatica "U. Dini"
viale Morgagni 65
Politecnico di Milano
Dipartimento di Matematica
Piazza Leonardo da Vinci 32
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).
Full version: pdf,
(Concerned with sequences
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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