A Note on Additive Bases of Abelian Groups of Rank 2.
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| 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] |
| Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 182356046 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Note on Additive Bases of Abelian Groups of Rank 2. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Qu%2C+Yongke%22">Qu, Yongke</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yongke1239@163.com</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Yuanlin%22">Li, Yuanlin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> yli@brocku.ca</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Qinghong%22">Wang, Qinghong</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> wqh1208@aliyun.com</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Xiaoyue%22">Zhao, Xiaoyue</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> zhaoxiaoyue76@163.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Graphs+%26+Combinatorics%22">Graphs & Combinatorics</searchLink>. Feb2025, Vol. 41 Issue 1, p1-8. 8p. – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00373-025-02895-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 1 Titles: – TitleFull: A Note on Additive Bases of Abelian Groups of Rank 2. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Qu, Yongke – PersonEntity: Name: NameFull: Li, Yuanlin – PersonEntity: Name: NameFull: Wang, Qinghong – PersonEntity: Name: NameFull: Zhao, Xiaoyue IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09110119 Numbering: – Type: volume Value: 41 – Type: issue Value: 1 Titles: – TitleFull: Graphs & Combinatorics Type: main |
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