Additive combinatorics | Additive number theory | Sumsets

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 S is the usual sumset which is denoted by nA if . When S is written as which is denoted by if . Note that |S| > 0 if and only if there exist with . (Wikipedia).

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From playlist Limits

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From playlist Calculus

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From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

Related pages

Additive number theory | Polynomial method in combinatorics | Kneser's theorem (combinatorics) | Sumset | Hans Heilbronn | Harold Davenport | Field (mathematics) | Combinatorics | Paul Erdős | Cyclic group | Modular arithmetic