Critical Sets in Equiorthogonal Frequency Squares
Abstract
In this paper, we study critical sets in pairs of equiorthogonal frequency squares. Using this stronger definition of orthogonality, a pair of equiorthogonal frequency squares is classified into one of three classes depending on the isomorphism or orthogonality of the corresponding rows and columns. We provide a general theorem determining the size of the critical set of a pair of equiorthogonal squares in which the corresponding rows and columns are isomorphic. For the other possible combinations of corresponding rows and columns, we make a few general observations with a detailed investigation into the conditions for the existence of an equiorthogonal mate and the size of a critical set for a pair of squares of order 8 based on 2 symbols.
Recommended Citation
I. H. Morgan and R. Saharay, "Critical Sets in Equiorthogonal Frequency Squares," Australasian Journal of Combinatorics, vol. 59, no. 1, pp. 182 - 205, Centre for Discrete Mathematics and Computing (University of Queensland), Jan 2014.
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
2202-3518; 1034-4942
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Centre for Discrete Mathematics and Computing (University of Queensland), All rights reserved.
Publication Date
01 Jan 2014
