Restricted sumset

In additive number theory and combinatorics, a restricted sumset has the form

where are finite nonempty subsets of a field F and is a polynomial over F.

If is a constant non-zero function, for example for any , then is the usual sumset which is denoted by if

When

S is written as which is denoted by if

Note that |S| > 0 if and only if there exist with