Duplicated Steiner triple systems with self-orthogonal near resolutions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913803700011008 |
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| author | Dukes, Peter J. Lamken, Esther R. |
| author_facet | Dukes, Peter J. Lamken, Esther R. |
| contents | A Steiner triple system, STS$(v)$, is a family of $3$-subsets (blocks) of a set of $v$ elements such that any two elements occur together in precisely one block. A collection of triples consisting of two copies of each block of an STS is called a duplicated Steiner triple system, DSTS. A resolvable (or near resolvable) DSTS is called self-orthogonal if every pair of distinct classes in the resolution has at most one block in common. We provide several methods to construct self-orthogonal near resolvable DSTS and settle the existence of such designs for all values of $v$ with only four possible exceptions. This addresses a recent question of Bryant, Davies and Neubecker. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duplicated Steiner triple systems with self-orthogonal near resolutions Dukes, Peter J. Lamken, Esther R. Combinatorics 05B07, 05B15 A Steiner triple system, STS$(v)$, is a family of $3$-subsets (blocks) of a set of $v$ elements such that any two elements occur together in precisely one block. A collection of triples consisting of two copies of each block of an STS is called a duplicated Steiner triple system, DSTS. A resolvable (or near resolvable) DSTS is called self-orthogonal if every pair of distinct classes in the resolution has at most one block in common. We provide several methods to construct self-orthogonal near resolvable DSTS and settle the existence of such designs for all values of $v$ with only four possible exceptions. This addresses a recent question of Bryant, Davies and Neubecker. |
| title | Duplicated Steiner triple systems with self-orthogonal near resolutions |
| topic | Combinatorics 05B07, 05B15 |
| url | https://arxiv.org/abs/2406.15614 |