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The Asymptotic Behaviour of Equidistant Permutation Arrays
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 45-48

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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┐(n 2 + n). In order to do this we require several more definitions. 
Vanstone, S. A. The Asymptotic Behaviour of Equidistant Permutation Arrays. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 45-48. doi: 10.4153/CJM-1979-005-0
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[1] 1. Bolton, D. W., unpublished manuscript. Google Scholar

[2] 2. Deza, M., Matrices dont deux lignes quelconques coincident dans un nombre donne de positions communes, Journal of Combinatorial Theory, Series A. 20 (1976), 306–318. Google Scholar

[3] 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] 4. Heinrich, K., van Rees, J., and Wallis, W. D., A general construction jor equidistant permutation arrays, (preprint). Google Scholar

[5] 5. Mullin, R. C., An asymptotic property of (r, λ)-systems, Utilitas Math. 3 (1973), 139–152. Google Scholar

[6] 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

[7] 7. Vanstone, S. A., Pairwise orthogonal generalized Room squares and equidistant permutation arrays, Journal of Combinatorial Theory, Series A. 25 (1978), 84–89. Google Scholar

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