Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T16:02:48.687Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive constructions for equidistant permutation arrays

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

P. J. Schellenberg  and
S. A. Vanstone
S. A. Vanstone
Affiliation:
University of Waterloo, Waterloo, Ontario
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An equidistant permutation array (EPA) is a ν × r array defined on an r-set, R, such that (i) each row is a permutation of the elements of R and (ii) any two distinct rows agree in λ positions (that is, the Hamming distance is (r−λ)).

Such an array is said to have order ν. In this paper we give several recursive constructions for EPA's.

The first construction uses a resolvable regular pairwise balanced design of order v to construct an EPA of order ν. The second construction is a generalization of the direct product construction for Room squares.

We also give a construction for intersection permutation arrays, which arrays are a generalization of EPA's.

MSC classification

Secondary: 05B30: Other designs, configurations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 2 , September 1977 , pp. 216 - 223
Copyright
Copyright © Australian Mathematical Society 1977

References

Baranyai, Z. (1975), On the factorization of the Complete Uniform Hypergraph, Infinite and Finite Sets, Vol. 1 (North Holland Publishing Co., Budapest, Hungary), pp. 91–108.Google Scholar
Deza, M. (1976), “Matrices dont deux lignes quelconques coincident dans un nombre donné de positions communes”, J. Combinatorial Theory (A) 20, 306–318.Google Scholar
Deza, M., Mullin, R. C. and Vanstone, S. A. (1976), “Room squares and equidistant permutation arrays”, Ars Combinatoria, 2, 235–244.Google Scholar
Heinrich, Katherine and van Rees, G. H. J. (to appear), “Some constructions for equidistant permutation arrays of index one”, Utilitas Mathematica.Google Scholar
Heinrich, Katherine, van Rees, G. H. J. and Wallis, W. D. (preprint), “A general construction for equidistant permutation arrays”.Google Scholar
Hughes, D. R. (1965), “On t-designs and groups”, Amer. J. Math. 87, 761–778.Google Scholar
Mullin, R. C. and Nemeth, E. (to appear), “An improved bound for equidistant permutation arrays of index one”, Utilitas Math.Google Scholar
Mullin, R. C. and Wallis, W. D. (1975), “The existence of Room squares”, Aequationes Math. 13, 1–7.Google Scholar
Ryser, H. J. (1963), Combinatorial Mathematics, The Carus Mathematical Monographs 14 (Mathematical Association of America).Google Scholar
Stanton, R. G. and Horton, J. D. (1972), “A multiplication theorem for Room squares”, J. Combinatorial Theory 12, 322–325.CrossRefGoogle Scholar
Vanstone, S. A. (to appear), “Pairwise orthogonal generalized Room squares and equidistant permutation arrays”, J. Combinatorial Theory (A).Google Scholar