Theorem in arithmetic combinatorics on finite partitions of the natural numbers
Folkman's theorem is a theorem in mathematics, and more particularly in arithmetic combinatorics and Ramsey theory. According to this theorem, whenever the natural numbers are partitioned into finitely many subsets, there exist arbitrarily large sets of numbers all of whose sums belong to the same subset of the partition.[1] The theorem had been discovered and proved independently by several mathematicians,[2][3] before it was named "Folkman's theorem", as a memorial to Jon Folkman, by Graham, Rothschild, and Spencer.[1]
^Rado, R. (1970), "Some partition theorems", Combinatorial theory and its applications, III: Proc. Colloq., Balatonfüred, 1969, Amsterdam: North-Holland, pp. 929–936, MR0297585.
^Sanders, Jon Henry (1968), A generalization of Schur's theorem, Ph.D. thesis, Yale University, MR2617864.