Additive properties of a pair of sequences
Fabricio Benevides, Jonathan Hulgan, Nathan Lemons, Cory Palmer, Ago-Erik Riet, Jeffrey Paul Wheeler (2009)
Acta Arithmetica
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Additive properties of a pair of sequences
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Let G be an additive abelian group of order k, and S be a sequence over G of length k+r, where 1 ≤ r ≤ k-1. We call the sum of k terms of S a k-sum. We show that if 0 is not a k-sum, then the number of k-sums is at least r+2 except for S containing only two distinct elements, in which case the number of k-sums equals r+1. This result improves the Bollobás-Leader theorem, which states that there are at least r+1 k-sums if 0 is not a k-sum.