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* Princeton Discrete Math Seminar *
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Speaker: David Conlon (CalTech)
Thursday 11th March, 3:00 via Zoom.
Title: Subset sums, completeness and colorings
Abstract: We develop novel techniques which allow us to prove a diverse
range of results relating to subset sums and complete sequences of positive
integers, including solutions to several longstanding open problems. These
include: solutions to three problems of Burr and Erdős on Ramsey complete
sequences, for which Erdős later offered a combined total of $350; analogous
results for the new notion of density complete sequences; the solution to a
conjecture of Alon and Erdős on the minimum number of colors needed to color
the positive integers less than n so that n cannot be written as a
monochromatic sum; the exact determination of an extremal function
introduced by Erdős and Graham on sets of integers avoiding a given subset
sum; and, answering a question of Tran, Vu and Wood, a homogeneous
strengthening of a seminal result of Szemerédi and Vu on long arithmetic
progressions in subset sums.
Joint work with Jacob Fox and Huy Tuan Pham.
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Next week: Stéphan Thomassé
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