A class of functions and their application in constructing semi-biplanes and association schemes

Coulter, R. S. and Henderson, M. (1999) A class of functions and their application in constructing semi-biplanes and association schemes. Discrete Mathematics, 202 1-3: 21-31.


Author Coulter, R. S.
Henderson, M.
Title A class of functions and their application in constructing semi-biplanes and association schemes
Journal name Discrete Mathematics   Check publisher's open access policy
Publication date 1999-05-06
Sub-type Article
DOI 10.1016/S0012-365X(98)00345-8
Volume number 202
Issue number 1-3
ISSN 0012-365X
Start page 21
End page 31
Total pages 11
Editor PL Hammer
Place of publication Amsterdam
Publisher Elsevier
Collection year 1999
Language eng
Subject C1
780101 Mathematical sciences
230102 Number Theory And Field Theory
Abstract We give an alternative proof of the fact that a planar function cannot exist on groups of even order. The argument involved leads us to define a class of functions which we call semi-planar. Through the introduction of an incidence structure we construct semi-biplanes using semi-planar functions. The method involved represents a new approach to constructing semi-biplanes and provides infinite classes of semi-biplanes unlike any known to the authors. For a particular class of semi-planar functions, we provide a method to construct association schemes with two associate classes. Such an association scheme is equivalent to a strongly regular graph. (C) 1999 Elsevier Science B.V. All rights reserved.
Keyword Mathematics
Semi-biplane
Association Scheme
Incidence Geometry
Semibiplanes
Q-Index Code C1

Document type: Journal Article
Sub-type: Article
Collection: School of Information Technology and Electrical Engineering Publications
 
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