4. Given positive integers $m, n$ satisfying $m \geq n \geq 2$, an injection $f:\{1,2, \ldots, n\} \rightarrow\{1,2, \ldots, m\}$, such that there exists a unique $i$, $i \in\{1,2, \ldots, n-1\}$, satisfying $f(i)>f(i+1)$, the number of such injections $f$ is $\qquad$
4. $C_{m}^{n}\left(2^{n}-n-1\right)$

Analysis: $f$ is an injection, the image set $A$ of $f$ has $C_{m}^{n}$, consider any one of them, without loss of generality, consider $A=\{1,2, \ldots, n\}$, i.e., the mapping $f:\{1,2, \ldots, n\} \rightarrow\{1,2, \ldots, n\}$, and there exists a unique $i$ such that $f(i)>f(i+1)$, thus it must satisfy $f(1)f(i+1)$, excluding the case $f(1)=1, f(2)=2, \ldots, f(i)=i$, so there are $\sum_{i=1}^{n-1}\left(C_{n}^{i}-1\right)=2^{n}-n-1$ cases in total. In summary, the number of injections $f$ is $C_{m}^{n}\left(2^{n}-n-1\right)$.