3-Group Divisible Designs with 3 Groups and Block Size 5
A 3-GDD (n, 2, k, λ1, λ2) was defined by combining the definitions of a group divisible design and a t-design. In this paper, we extend the definitions to 3 groups and block size 5, and we denote such GDD by 3-GDD (n, 3, 5, μ1, μ2). Some necessary conditions for the existence of these GDDs are devel...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/1010091 |
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| _version_ | 1832559528856518656 |
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| author | Zebene Girma Tefera Dinesh G. Sarvate Samuel Asefa Fufa |
| author_facet | Zebene Girma Tefera Dinesh G. Sarvate Samuel Asefa Fufa |
| author_sort | Zebene Girma Tefera |
| collection | DOAJ |
| description | A 3-GDD (n, 2, k, λ1, λ2) was defined by combining the definitions of a group divisible design and a t-design. In this paper, we extend the definitions to 3 groups and block size 5, and we denote such GDD by 3-GDD (n, 3, 5, μ1, μ2). Some necessary conditions for the existence of these GDDs are developed, and several new constructions and specific instances of nonexistence are given. |
| format | Article |
| id | doaj-art-f4f4006363814e669170da4f2206627d |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f4f4006363814e669170da4f2206627d2025-02-03T01:29:51ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/10100913-Group Divisible Designs with 3 Groups and Block Size 5Zebene Girma Tefera0Dinesh G. Sarvate1Samuel Asefa Fufa2Department of MathematicsCollege of CharlestonDepartment of MathematicsA 3-GDD (n, 2, k, λ1, λ2) was defined by combining the definitions of a group divisible design and a t-design. In this paper, we extend the definitions to 3 groups and block size 5, and we denote such GDD by 3-GDD (n, 3, 5, μ1, μ2). Some necessary conditions for the existence of these GDDs are developed, and several new constructions and specific instances of nonexistence are given.http://dx.doi.org/10.1155/2023/1010091 |
| spellingShingle | Zebene Girma Tefera Dinesh G. Sarvate Samuel Asefa Fufa 3-Group Divisible Designs with 3 Groups and Block Size 5 Journal of Mathematics |
| title | 3-Group Divisible Designs with 3 Groups and Block Size 5 |
| title_full | 3-Group Divisible Designs with 3 Groups and Block Size 5 |
| title_fullStr | 3-Group Divisible Designs with 3 Groups and Block Size 5 |
| title_full_unstemmed | 3-Group Divisible Designs with 3 Groups and Block Size 5 |
| title_short | 3-Group Divisible Designs with 3 Groups and Block Size 5 |
| title_sort | 3 group divisible designs with 3 groups and block size 5 |
| url | http://dx.doi.org/10.1155/2023/1010091 |
| work_keys_str_mv | AT zebenegirmatefera 3groupdivisibledesignswith3groupsandblocksize5 AT dineshgsarvate 3groupdivisibledesignswith3groupsandblocksize5 AT samuelasefafufa 3groupdivisibledesignswith3groupsandblocksize5 |