Combinatorial interpretations of elementary symmetric polynomials? I have some questions as to some good combinatorial interpretations for the sum of elementary symmetric polynomials. I know that for example, for n =2 we have that:
$e_0  = 1$
$e_1 = x_1+x_2$
$e_2 = x_1x_2$
And each of these can clearly been seen as the coefficient of $t^k$ in $(1+x_1t)(1+x_2t)$. Now, in general, what combinatorial interpreations are there for say:
$\sum_{i=0}^n e_i(x)$ for some $x = (x_1,...,x_n)$ ? 

A term in $e_k$ is the set of combinations of size $i$ from a set of size $n$. So the coefficient of a term in $\sum_{k=0} e_k$ is the number of combinations of -all- sizes, or rather, there is a one-to-one correspondence with the terms in the sum with the subsets of a set of size $n$. 
