Sumset of a field subject to a specific polynomial restriction
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