Enumeration of saturated chains in Dyck lattices
arXiv:1203.6807 · doi:10.1016/j.aam.2014.09.003
Abstract
We determine a general formula to compute the number of saturated chains in Dyck lattices, and we apply it to find the number of saturated chains of length 2 and 3. We also compute what we call the Hasse index (of order 2 and 3) of Dyck lattices, which is the ratio between the total number of saturated chains (of length 2 and 3) and the cardinality of the underlying poset.
9 pages