  In this paper, we study pattern avoidances of generalized permutations and
show that the number of all generalized permutations avoiding $\pi$ is
independent of the choice of $\pi\in S_3$, which extends the classic results on
permutations avoiding $\pi\in S_3$. Extending both Dyck path and Riordan path,
we introduce the Catalan-Riordan path which turns out to be a combinatorial
interpretation of the difference array of Catalan numbers. As applications, we
interpret both Motzkin and Riordan numbers in two ways, via semistandard Young
tableaux of two rows and generalized permutations avoiding $\pi \in S_3$.
Analogous to Lewis's method, we establish a bijection from generalized
permutations to rectangular semistandard Young tableaux which will recover
several known results in the literature.
