Complete Sets of Mutually Orthogonal Hypercubes and Their Connections to Affine Resolvable Designs
Abstract
Recently, Laywine and Mullen proved several generalizations of Bose's equivalence between the existence of complete sets of mutually orthogonal Latin squares of order n and the existence of affine planes of order n. Laywine further investigated the relationship between sets of orthogonal frequency squares and affine resolvable balanced incomplete block designs. In this paper we generalize several of Laywine's results that were derived for frequency squares. We provide sufficient conditions for construction of an affine resolvable design from a complete set of mutually orthogonal Youden frequency hypercubes; we also show that, starting with a complete set of mutually equiorthogonal frequency hypercubes, an analogous construction can always be done. In addition, we give conditions under which an affine resolvable design can be converted to a complete set of mutually orthogonal Youden frequency hypercubes or a complete set of mutually equiorthogonal frequency hypercubes.
Recommended Citation
I. H. Morgan, "Complete Sets of Mutually Orthogonal Hypercubes and Their Connections to Affine Resolvable Designs," Annals of Combinatorics, Springer Verlag, Jan 2001.
The definitive version is available at https://doi.org/10.1007/s00026-001-8009-5
Department(s)
Mathematics and Statistics
Keywords and Phrases
frequency hypercubes; affine resolvable balanced incomplete block designs; prime blocks
International Standard Serial Number (ISSN)
0218-0006
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2001 Springer Verlag, All rights reserved.
Publication Date
01 Jan 2001
