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Bounds for Folkman’s Theorem

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Bounds for Folkman’s Theorem
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Folkman’s theorem asserts that in any red-blue colouring of [N], there is an n-set all of whose finite sums are the same colour. How large must N be in terms of n? Improving on Erdos—Spencer from the 80s, I’ll show that N must be at least doubly exponential in n.