2008Unpublished venueRequires access

On sumfree subsets of hypercubes

Daniel J. Katz

Open publisher page 1 citations

Abstract

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. 1

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What this paper is about

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. 1

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Available abstract

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. 1

Key concepts: Hypercube, Mathematics, Upper and lower bounds, Generalization, Combinatorics, Discrete mathematics, Mathematical analysis

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