2024/07/09 by Yuta Watanabe, Watanabe, Yuta
Mathematics · #05E30 #15A72 #33D50 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2407.06550
openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.