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A characterization of sequences with the minimum number of k-sums modulo k

100%

Xia X., Qu Y., Qian G.

Colloquium Mathematicum

2014

tom 136

nr 1

51-56

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.

On additive bases II

88%

Gao W., Han D., Qian G., Qu Y., Zhang H.

Acta Arithmetica

2015

tom 168

nr 3

247-267

Let G be an additive finite abelian group, and let S be a sequence over G. We say that S is regular if for every proper subgroup H ⊆ G, S contains at most |H|-1 terms from H. Let 𝖼₀(G) be the smallest integer t such that every regular sequence S over G of length |S| ≥ t forms an additive basis of G, i.e., every element of G can be expressed as the sum over a nonempty subsequence of S. The constant 𝖼₀(G) has been determined previously only for the elementary abelian groups. In this paper, we determine 𝖼₀(G) for some groups including the cyclic groups, the groups of even order, the groups of rank at least five, and all the p-groups except $G=C_p ⊕ C_{p^n}$ with n≥ 2.

Ograniczanie wyników

1 Acta Arithmetica

1 Colloquium Mathematicum

2 Qian G.

2 Qu Y.

1 Gao W.

1 Han D.

1 Xia X.

1 Zhang H.

1 2015

1 2014

Wyniki wyszukiwania

A characterization of sequences with the minimum number of k-sums modulo k

On additive bases II