Geodesic
A characterization of sequences with the minimum number of $k$-sums modulo $k$
Xingwu Xia1 ; Yongke Qu1 ; Guoyou Qian2
1 Department of Mathematics Luoyang Normal University LuoYang 471022, P.R. China
2 Mathematical College Sichuan University Chengdu 610064, P.R. China
Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 51-56.

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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 $1\le r\le k-1$. 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.
DOI : 10.4064/cm136-1-5
Keywords: additive abelian group order sequence length where k call sum terms k sum k sum number k sums least except containing only distinct elements which number k sums equals result improves bollob leader theorem which states there least k sums k sum

Xingwu Xia 1 ; Yongke Qu 1 ; Guoyou Qian 2

1 Department of Mathematics Luoyang Normal University LuoYang 471022, P.R. China
2 Mathematical College Sichuan University Chengdu 610064, P.R. China 
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Xingwu Xia; Yongke Qu; Guoyou Qian. A characterization of sequences with the minimum number of $k$-sums modulo $k$. Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 51-56. doi : 10.4064/cm136-1-5. http://geodesic.mathdoc.fr/articles/10.4064/cm136-1-5/

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