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

Xingwu Xia, Yongke Qu, and Guoyou Qian. "A characterization of sequences with the minimum number of k-sums modulo k." Colloquium Mathematicae 136.1 (2014): 51-56. <http://eudml.org/doc/284237>.

@article{XingwuXia2014,
abstract = {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.},
author = {Xingwu Xia, Yongke Qu, Guoyou Qian},
journal = {Colloquium Mathematicae},
keywords = {k-sum; finite abelian group; zero-sum sequence},
language = {eng},
number = {1},
pages = {51-56},
title = {A characterization of sequences with the minimum number of k-sums modulo k},
url = {http://eudml.org/doc/284237},
volume = {136},
year = {2014},
}

TY - JOUR
AU - Xingwu Xia
AU - Yongke Qu
AU - Guoyou Qian
TI - A characterization of sequences with the minimum number of k-sums modulo k
JO - Colloquium Mathematicae
PY - 2014
VL - 136
IS - 1
SP - 51
EP - 56
AB - 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.
LA - eng
KW - k-sum; finite abelian group; zero-sum sequence
UR - http://eudml.org/doc/284237
ER -