Statistics of Partial Permutations via Catalan matrices

Yen-Jen Cheng, Sen-Peng Eu, Hsiang-Chun Hsu

A generalized Catalan matrix $(a_{n,k}{)}_{n,k\ge 0}$ is generated by two seed sequences $\mathbf{s}=(s_0,s_1,\dots )$ and $\mathbf{t}=(t_1,t_2,\dots )$ together with a recurrence re…