Notation for a string of objects Is there a commonly used notation for a string of objects? The particular situation I am interested in is a string of elements from a Boolean algebra. The elements in the string may be expressions using the Boolean operations $\wedge$ and $\vee$. When this situation occurs I enclose such an element in parentheses. A typical example of such a string is
$$(a_{1} \wedge b_{1}) \ldots (a_{m} \wedge b_{1}) (a_{1} \wedge b_{2}) \ldots (a_{m} \wedge b_{2}) \ldots (a_{1} \wedge b_{n}) \ldots (a_{m} \wedge b_{n})$$
What I would like is something like a summation sign so that I could save space and improve clarity. So that this string could be written in a manner similar to
$$\sum_{i = 1}^{m}\sum_{j = 1}^{n} (a_{i} \wedge b_{j}) \text{,}$$
but without the implied operation of addition.

Hint: A commonly used notation for creating strings is concatenation of letters taken from an alphabet $V$.
We could then write
\begin{align*}
&(a_{1} \wedge b_{1}) \ldots (a_{m} \wedge b_{1}) (a_{1} \wedge b_{2}) \ldots (a_{m} \wedge b_{2}) \ldots (a_{1} \wedge b_{n}) \ldots (a_{m} \wedge b_{n})\\
&\qquad=\prod_{l=1}^n\prod_{k=1}^m(a_{k} \wedge b_{l}) 
\end{align*}
where non-commutativity of concatenation has to be appropriately addressed.
