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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.16444 |
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| _version_ | 1866917703385612288 |
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| author | Jäger, Gerold Markström, Klas Öhman, Lars-Daniel Shcherbak, Denys |
| author_facet | Jäger, Gerold Markström, Klas Öhman, Lars-Daniel Shcherbak, Denys |
| contents | We computationally completely enumerate a number of types of row-column designs up to isotopism, including double, sesqui and triple arrays as known from the literature, and two newly introduced types that we call mono arrays and AO-arrays. We calculate autotopism group sizes for the designs we generate. For larger parameter values, where complete enumeration is not feasible, we generate examples of some of the designs, and generate exhaustive lists of admissible parameters. For some admissible parameter sets, we prove non-existence results. We also give some explicit constructions of sesqui arrays, mono arrays and AO-arrays, and investigate connections to Youden rectangles and binary pseud Youden designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16444 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumeration of Row-Column Designs Jäger, Gerold Markström, Klas Öhman, Lars-Daniel Shcherbak, Denys Combinatorics Discrete Mathematics Statistics Theory We computationally completely enumerate a number of types of row-column designs up to isotopism, including double, sesqui and triple arrays as known from the literature, and two newly introduced types that we call mono arrays and AO-arrays. We calculate autotopism group sizes for the designs we generate. For larger parameter values, where complete enumeration is not feasible, we generate examples of some of the designs, and generate exhaustive lists of admissible parameters. For some admissible parameter sets, we prove non-existence results. We also give some explicit constructions of sesqui arrays, mono arrays and AO-arrays, and investigate connections to Youden rectangles and binary pseud Youden designs. |
| title | Enumeration of Row-Column Designs |
| topic | Combinatorics Discrete Mathematics Statistics Theory |
| url | https://arxiv.org/abs/2406.16444 |