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

### Tom 136 / 2014

Colloquium Mathematicum 136 (2014), 51-56 MSC: Primary 11B30; Secondary 11B50. DOI: 10.4064/cm136-1-5

#### Streszczenie

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.

#### Autorzy

Luoyang Normal University
LuoYang 471022, P.R. China
e-mail
• Yongke QuDepartment of Mathematics
Luoyang Normal University
LuoYang 471022, P.R. China
e-mail
• Guoyou QianMathematical College
Sichuan University
Chengdu 610064, P.R. China
e-mail
e-mail

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