Zero-sum problems in finite abelian groups and affine caps
Zero-sum problems in finite abelian groups and affine caps
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DOI：
10.1093/qmath/ham003
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发表时间：
2007-06-01
影响因子：
0.7
通讯作者：
Rackham, Laurence
中科院分区：
文献类型：
--
作者：
Edel, Yves;Elsholtz, Christian;Rackham, Laurence
对于有限阿贝尔群G，设S（G）表示最小整数I，使得G上的每个长度为S vertical bar >= 1的序列S都有一个长度为exp（G）的零和子序列.我们得到了S（G）的新的上界和下界，并且对于特殊类型的群，我们的所有界都是尖锐的。这些结果并不局限于G = C-n（r）形式的群G，但它们考虑了群的结构。特别地，我们证明了对所有奇数n，S（C-n（4））>= 20 n- 19，当n是3的幂时，S（C-n（4））是尖锐的.此外，我们还研究了有限几何中极值序列与极大帽之间的关系。
For a finite abelian group G, let S(G) denote the smallest integer I such that every sequence S over G of length vertical bar S vertical bar >= 1 has a zero-sum subsequence of length exp(G). We derive new upper and lower bounds for S(G), and all our bounds are sharp for special types of groups. The results are not restricted to groups G of the form G = C-n(r), but they respect the structure of the group. In particular, we Show S(C-n(4)) >= 20n - 19 for all odd n, which is sharp if n is a power of 3. Moreover, we investigate the relationship between extremal sequences and maximal caps in finite geometry.