Two combinatorial statistics on Dyck paths
نویسندگان
چکیده
منابع مشابه
Two Statistics Linking Dyck Paths and Non-crossing Partitions
We introduce a pair of statistics, maj and sh, on Dyck paths and show that they are equidistributed. Then we prove that this maj is equivalent to the statistics ls and rb on non-crossing partitions. Based on non-crossing partitions, we give the most obvious q-analogue of the Narayana numbers and the Catalan numbers.
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The Catalan number has a lot of interpretations and one of them is the number of Dyck paths. A Dyck path is a lattice path from (0, 0) to (n, n) which is below the diagonal line y = x. One way to generalize the definition of Dyck path is to change the end point of Dyck path, i.e. we define (generalized) Dyck path to be a lattice path from (0, 0) to (m, n) ∈ N2 which is below the diagonal line y...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0147-v