On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations

Document Type

Article

Publication Date

1-1-2006

Abstract

For a given non-symmetric commutative association scheme, by fusing all the non-symmetric relations pairwise with their symmetric counterparts, we can obtain a new symmetric association scheme. In this paper, we introduce a set of feasibility and realizability conditions for a class e symmetric association scheme to be split into a class e + 1 non-symmetric commutative association scheme. By applying the feasibility and realizability conditions, we obtain a classification into six categories of the class 4 non-symmetric fission schemes of group-divisible 3-schemes. Complete solutions for three of the six categories and partial results for the remaining cases are presented. © 2006 Elsevier B.V. All rights reserved.

Keywords

Non-symmetric commutative association scheme, Fusion, Fission, Hadamard matrix

Publication Title

Discrete Mathematics

ISSN

0012-365X

Divisions

MathematicalSciences

Volume

306

Issue

24

Publisher

Elsevier

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