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arXiv · 2407.06550

Terwilliger Algebra of the Ordered Hamming Scheme

Yuta Watanabe
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Abstract

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.

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Yuta Watanabe. 2024-07-09. Terwilliger Algebra of the Ordered Hamming Scheme. https://arxiv.org/abs/2407.06550

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