Let
$$ \Sigma = \left\{ s_1,\ldots, s_n \right\} $$
For fixed $1 \leq k \leq n$ there I have $\binom{n}{k}$ possible combination of substrings that don't count repetition and order,etc. Is there a way to denote the generic subset of $\Sigma$ having these $\binom{n}{k}$ elements?
The purpose would be to write as summation the following product
$$ f(\delta_1,\ldots,\delta_n) = \prod_{i=1}^{n} (1+\delta_i) $$
Following the comments:
Could be the following correct?
$$ f(\delta_1,...,\delta_n) = 1 + \sum_{k=1}^{n} \binom{n}{k} \sum_{\begin{array}{l} J \subset \cal{P}(\left\{1,...,n \right\}) \\ card \; J = k \end{array}}\delta_{J(1)} ...\delta_{J(k)} $$