Is there a common notation for the set of all injections from $A$ into $B$?

Some set-theorists use $B^{(A)}$, e.g., A. Levy in his book *Basic Set Theory*.

But some combinatorists use $B^{\underline{A}}$ or $(B)_A$, e.g. JMoravitz's answer in this question.

Some other combinatorists also use $\mathrm{Inj}(A,B)$, e.g., M. Aigner in his book *Combinatorial Theory*. But I don't like a notation of this kind, since I want something similar to $B^A$ or ${}^AB$ which is commonly used to denote the set of all maps from $A$ to $B$.

Any suggestions for a notation are welcome.