Bibliographic Details
| Title: |
A Note on Additive Bases of Abelian Groups of Rank 2. |
| Authors: |
Qu, Yongke1 (AUTHOR) yongke1239@163.com, Li, Yuanlin2 (AUTHOR) yli@brocku.ca, Wang, Qinghong3 (AUTHOR) wqh1208@aliyun.com, Zhao, Xiaoyue4 (AUTHOR) zhaoxiaoyue76@163.com |
| Source: |
Graphs & Combinatorics. Feb2025, Vol. 41 Issue 1, p1-8. 8p. |
| Abstract: |
Let G be a finite abelian group and p be the smallest prime divisor of |G|. Let S be a sequence over G. We say that S is regular if S contains at most | H | - 1 terms from H for every proper subgroup H ⊊ G . Let c 0 (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., ∑ (S) = G . It was conjectured by Gao et al. [2] that c 0 (G) = m (G) . In this note, we confirm the conjecture for the case when G = C n 1 ⊕ C n 2 with n 1 | n 2 , p ≥ 11 and n 1 ≥ p 2 and we also characterize the structure of regular sequences S over G of length | S | = c 0 (G) - 1 with ∑ (S) ≠ G . [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
