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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: Chia, Gek Ling, Kok, Wai Keong
Format: Article
Published: Elsevier 2006
Subjects:
Q Science (General)
QA Mathematics
Online Access:http://eprints.um.edu.my/25660/
https://doi.org/10.1016/j.disc.2006.06.005
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spelling my.um.eprints.256602020-12-17T01:34:33Z http://eprints.um.edu.my/25660/ On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations Chia, Gek Ling Kok, Wai Keong Q Science (General) QA Mathematics 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. Elsevier 2006 Article PeerReviewed Chia, Gek Ling and Kok, Wai Keong (2006) On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations. Discrete Mathematics, 306 (24). pp. 3189-3222. ISSN 0012-365X https://doi.org/10.1016/j.disc.2006.06.005 doi:10.1016/j.disc.2006.06.005
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic Q Science (General)
QA Mathematics
spellingShingle Q Science (General)
QA Mathematics
Chia, Gek Ling
Kok, Wai Keong
On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
description 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.
format Article
author Chia, Gek Ling
Kok, Wai Keong
author_facet Chia, Gek Ling
Kok, Wai Keong
author_sort Chia, Gek Ling
title On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
title_short On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
title_full On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
title_fullStr On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
title_full_unstemmed On non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
title_sort on non-symmetric commutative association schemes with exactly one pair of non-symmetric relations
publisher Elsevier
publishDate 2006
url http://eprints.um.edu.my/25660/
https://doi.org/10.1016/j.disc.2006.06.005
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score 13.188404

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