Statistics of partial permutations via Catalan matrices

A generalized Catalan matrix ( a n , k ) ≥ 0 is generated by two seed sequences s = 1 … and t 2 together with recurrence relation. By taking ℓ + we can interpret as the number of partial permutations, which are × -matrices zero rows at most one in each row or column. In this paper prove that fundamental statistics some set-valued on permutations also be defined encoded sequences. Results interesting permutation families, namely connected cycle-up-down given.