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On the Terwilliger Algebra of the Group Association Scheme of the Symmetric Group Sym ( 7 )
Author(s) -
Herman Allen,
Maleki Roghayeh,
Razafimahatratra Andriaherimanana Sarobidy
Publication year - 2025
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21981
Subject(s) - mathematics , association scheme , group (periodic table) , symmetric group , scheme (mathematics) , combinatorics , algebra over a field , pure mathematics , chemistry , organic chemistry , mathematical analysis
ABSTRACT Terwilliger algebras are finite‐dimensional semisimple algebras that were first introduced by Paul Terwilliger in 1992 in studies of association schemes and distance‐regular graphs. The Terwilliger algebras of the conjugacy class association schemes of the symmetric groupsSym ( n ), for3 ≤ n ≤ 6, have been studied and completely determined. The case forSym ( 7 )is computationally much more difficult and has a potential application to find the size of the largest permutation codes ofSym ( 7 )with a minimal distance of at least 4. In this paper, the dimension, the Wedderburn decomposition, and the block dimension decomposition of the Terwilliger algebra of the conjugacy class scheme of the groupSym ( 7 )are determined.