Additive Combinatorics Definition


A subbranch of combinatorics that concerns additive problems expressed using sumsets.

One major area of study in additive combinatorics is that of inverse problems: for instance, given the sumset A + B is small in size, what can we say about the structures of A and B? In the case of integer sumsets, Freiman's theorem provides a partial answer.

Origin of Additive Combinatorics

  • Coined circa early 2000s by Australian -American mathematician Terence Tao for a rapidly developing field growing out of combinatorial number theory , named differently to reflect a changed emphasis in the problems being studied.

    From Wiktionary

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