Abstract
Two permutations on n elements are at (Hamming) distance μ if they disagree in exactly μ places. An equidistant permutation array is a collection of permutations on n elements, every pair of which is at distance μ. A permutation graph G(n,μ) is a graph with vertex set comprising all permutations on n elements, and edges between each pair of permutations at distance μ. These graphs enable the relevant permutation structure to be visualised; in particular, the cliques correspond to maximal equidistant permutation arrays. We obtain various structural theorems for these graphs, and conjecture several properties for their cliques.
Keywords
- Conjugacy Class
- Cayley Graph
- Maximum Clique
- Complete Subgraph
- Permutation Graph
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References
D.W. Bolton, "Problem", Combinatorics, ed. D.Y.A. Welsh and D.R. Woodall, Math. Inst. Oxford (1972), pp.351–352.
J. Dénes, "Latin squares and codes", to appear in Proc. Internat. Conf. on Information Theory, Paris, July 1977.
M. Deza, R.C. Mullin and S.A. Vanstone, "Room squares and equidistant permutation arrays", Ars Combinatoria 2 (1976), 235–244.
Katherine Heinrich, G.H.J. van Rees and W.D. Wallis, "A general construction for equidistant permutation arrays", to appear in Graph Theory and Related Topics, Proc. of Conf. on Graph Theory, Waterloo, July 1977.
R.C. Mullin, "An asymptotic property of (r,λ)-systems", Utilitas Math. 3 (1973), 139–152.
John Riordan, An Introduction to Combinatorial Analysis, Wiley (1958).
S.A. Vanstone, "The asymptotic behaviour of equidistant permutation arrays", submitted to Canad. J. Math.
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© 1978 Springer-Verlag
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Eggleton, R.B., Hartman, A. (1978). A note on equidistant permutation arrays. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062526
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DOI: https://doi.org/10.1007/BFb0062526
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08953-7
Online ISBN: 978-3-540-35702-5
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