Maximum value of symmetric elementary polynomials?

Question

Assume a function $f(a_1,a_2,...,a_t)$ over the $t$ variables $a_i$ (each $a_i$ is $N$-bit). I read that if for such functions it holds that $|f(a_1,a_2,...,a_t)|<l$, where $l$ assume it's a correctness limit, then this is equivalent as if we handle elementrary symmetric polynomials of degree $d$ in $t$ variables, as long as $2^{Nd} \cdot$$t \choose d $$<l$. Can you explain to me how the quantity $2^{Nd} \cdot$$t \choose d $ occurs?

Answer 1

Better late than never. If someone sees the definition of elementary symmetric polynomials of degree $d$ with $t$ variables and assumes that each variable is $N$-bits then there are

$t \choose d $ terms in the polynomial, each one being maximum $2^N$ and thus due to the degree $d$ we have maximum $2^{Nd}$. Putting all the terms together to calculate the max value we have $2^{Nd}$ $t \choose d $