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The Asymptotic Behaviour of Equidistant Permutation Arrays

Published online by Cambridge University Press:  20 November 2018

S. A. Vanstone
S. A. Vanstone*
Affiliation:
St. Jerome's College, University of Waterloo, Waterloo, Ontario
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An equidistant permutation array (EPA) A(r λ v) is a v × r array defined on a set V of r symbols such that every row is a permutation of V and any two distinct rows have precisely λ common column entries. Define R(r, λ) to be the largest value of v for which there exists an A (r, λ; v). Deza [2] has shown that

where n = r – λ. Bolton [1] has shown that

(*)

In this paper, we show that equality holds in (*) for λ > ┌n/3┐(n2 + n). In order to do this we require several more definitions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 45 - 48
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Bolton, D. W., unpublished manuscript.Google Scholar
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3. Deza, M., Mullin, R. C. and Vanstone, S. A., Room squares and equidistant permutation arrays, Ars Combinatori. 2 (1976), 235–244.Google Scholar
4. Heinrich, K., van Rees, J., and Wallis, W. D., A general construction jor equidistant permutation arrays, (preprint).Google Scholar
5. Mullin, R. C., An asymptotic property of (r, λ)-systems, Utilitas Math. 3 (1973), 139–152.Google Scholar
6. Schellenberg, P. J., and Vanstone, S. A., Some results on equidistant permutation arrays, Proc. 6th Manitoba Conference on Numerical Math (1976), 389–410.Google Scholar
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