Terwilliger Algebra of the Ordered Hamming Scheme
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913422759690240 |
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| author | Watanabe, Yuta |
| author_facet | Watanabe, Yuta |
| contents | This paper delves into the Terwilliger algebra associated with the ordered Hamming scheme, which extends from the wreath product of one-class association schemes and was initially introduced by Delsarte as a natural expansion of the Hamming schemes. Levstein, Maldonado and Penazzi have shown that the Terwilliger algebra of the Hamming scheme of length $n$ is the $n$-fold symmetric tensor algebra of that of the one-class association scheme. Furthermore, Bhattacharyya, Song and Tanaka have established that the Terwilliger algebra of the wreath product of a one-class association scheme is a direct sum of the ``primary'' subalgebra and commutative subalgebras. This paper extends these findings to encompass both conclusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Terwilliger Algebra of the Ordered Hamming Scheme Watanabe, Yuta Combinatorics 05E30, 15A72, 33D50 This paper delves into the Terwilliger algebra associated with the ordered Hamming scheme, which extends from the wreath product of one-class association schemes and was initially introduced by Delsarte as a natural expansion of the Hamming schemes. Levstein, Maldonado and Penazzi have shown that the Terwilliger algebra of the Hamming scheme of length $n$ is the $n$-fold symmetric tensor algebra of that of the one-class association scheme. Furthermore, Bhattacharyya, Song and Tanaka have established that the Terwilliger algebra of the wreath product of a one-class association scheme is a direct sum of the ``primary'' subalgebra and commutative subalgebras. This paper extends these findings to encompass both conclusions. |
| title | Terwilliger Algebra of the Ordered Hamming Scheme |
| topic | Combinatorics 05E30, 15A72, 33D50 |
| url | https://arxiv.org/abs/2407.06550 |