On sumfree subsets of hypercubes

Daniel J. Katz
2009 Acta Arithmetica  
We consider the possible sizes of large sumfree sets contained in the discrete hypercube $\{1,...,n\}^k$, and we determine upper and lower bounds for the maximal size as $n$ becomes large. We also discuss a continuous analogue in which our lower bound remains valid and our upper bound can be strengthened, and we consider the generalization of both problems to $l$-fold-sumfree sets.
doi:10.4064/aa137-2-3 fatcat:kes6lsvmcnbq5neojfcgmiz42i