On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
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 asso...
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| Main Authors: | , |
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| Format: | Article |
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Elsevier
2006
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| Subjects: | |
| Online Access: | http://eprints.um.edu.my/25660/ https://doi.org/10.1016/j.disc.2006.06.005 |
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| Summary: | 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. |
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