We find a closed formula for the number of chains in Dyck lattices. Moreover, we determine a general formula to compute the number of saturated chains, and we apply it to find the number of saturated chains of length 2, 3 and 4. We also compute what we call the Hasse index (of order 2, 3 and 4) of Dyck lattices, which is the ratio between the total number of saturated chains (of length 2, 3 and 4) and the cardinality of the underlying poset.
Enumeration of chains and saturated chains in Dyck lattices
FERRARI, LUCA;MUNARINI, EMANUELE
2015-01-01
Abstract
We find a closed formula for the number of chains in Dyck lattices. Moreover, we determine a general formula to compute the number of saturated chains, and we apply it to find the number of saturated chains of length 2, 3 and 4. We also compute what we call the Hasse index (of order 2, 3 and 4) of Dyck lattices, which is the ratio between the total number of saturated chains (of length 2, 3 and 4) and the cardinality of the underlying poset.File in questo prodotto:
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