Premium
On the dimension of affine resolvable designs and hypercubes
Author(s) -
Laywine Charles F.
Publication year - 1996
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1996)4:4<235::aid-jcd2>3.0.co;2-g
Subject(s) - hypercube , mathematics , affine transformation , combinatorics , equivalence (formal languages) , prime (order theory) , dimension (graph theory) , block design , discrete mathematics , pure mathematics
The equivalence between complete sets of mutually orthogonal hypercubes and affine resolvable designs, which generalizes the well‐known equivalence between complete sets of mutually orthogonal latin squares and affine planes, is used to examine the dimension of designs by studying the prime classes in the associated hypercubes. Particular attention is given to designs of order n =9 including a design which is nonisomorphic to AG(3, 9) even though it possesses the same parameters and three prime classes. © 1996 John Wiley & Sons, Inc.