The Terwilliger algebras of doubly regular tournaments
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916210503843840 |
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| author | Herman, Allen |
| author_facet | Herman, Allen |
| contents | The Terwilliger algebras of asymmetric association schemes of rank $3$, whose nonidentity relations correspond to doubly regular tournaments, are shown to have thin irreducible modules, and to always be of dimension $4k+9$ for some positive integer $k$. It is determined that asymmetric rank $3$ association schemes of order up to $23$ are determined up to combinatorial isomorphism by the list of their complex Terwilliger algebras at each vertex, but this no longer true at order $27$. To distinguish order $27$ asymmetric rank $3$ association schemes, it is shown using computer calculations that the list of rational Terwilliger algebras at each vertex will suffice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Terwilliger algebras of doubly regular tournaments Herman, Allen Combinatorics Rings and Algebras 05E30 (Primary) 16S99, 05C20, 05C50 (Secondary) The Terwilliger algebras of asymmetric association schemes of rank $3$, whose nonidentity relations correspond to doubly regular tournaments, are shown to have thin irreducible modules, and to always be of dimension $4k+9$ for some positive integer $k$. It is determined that asymmetric rank $3$ association schemes of order up to $23$ are determined up to combinatorial isomorphism by the list of their complex Terwilliger algebras at each vertex, but this no longer true at order $27$. To distinguish order $27$ asymmetric rank $3$ association schemes, it is shown using computer calculations that the list of rational Terwilliger algebras at each vertex will suffice. |
| title | The Terwilliger algebras of doubly regular tournaments |
| topic | Combinatorics Rings and Algebras 05E30 (Primary) 16S99, 05C20, 05C50 (Secondary) |
| url | https://arxiv.org/abs/2404.11560 |