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](https://math.stackexchange.com/questions/1896815).


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.



Notation for the set of all injections from $A$ into $B$
The notation suggested by cardinal equalities such as


\begin{array}{l|l|l}
\text{concept} & \text{notation} & \text{cardinality} \\
\hline
\text{disjoint union of $A$ and $B$} & A + B & |A + B| = |A| + |B| \\
\text{Cartesian product of $A$ and $B$} & A \times B & |A \times B| = |A| \times |B| \\
\text{set of functions from $A$ to $B$, also $A \rightarrow B$} & B^A & |B^A| = |B|^{|A|} \\
\text{set of permutations of $A$, also $\text{Sym}(A)$} & A! & |A!| = |A|! \\
\text{set of $k$-element subsets of $A$} & \binom{A}{k} & \left|\binom{A}{k}\right| = \binom{|A|}{k} \\
\text{set of $k$-element partitions of $A$} & \left\{{A \atop k}\right\} & \left| \left\{{A \atop k}\right\} \right| = \left\{{|A| \atop k}\right\}
\end{array}


is


\begin{array}{l|l|l}
\text{concept} & \text{notation} & \text{cardinality} \\
\hline
\text{set of injections from $A$ to $B$} & B^{\underline{A}} & |B^{\underline{A}}| = |B|^{\underline{|A|}}
\end{array}


because the [falling factorial](https://en.wikipedia.org/wiki/Falling_and_rising_factorials#Properties)


\begin{align\*}
|B|^\underline{|A|} = \frac{|B|!}{(|B| - |A|)!}
\end{align\*}


is precisely [the number of injections](https://math.stackexchange.com/a/1529415) from $A$ to $B$.


