Skip to main content

A note on equidistant permutation arrays

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 686)

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

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.W. Bolton, "Problem", Combinatorics, ed. D.Y.A. Welsh and D.R. Woodall, Math. Inst. Oxford (1972), pp.351–352.

    Google Scholar 

  2. J. Dénes, "Latin squares and codes", to appear in Proc. Internat. Conf. on Information Theory, Paris, July 1977.

    Google Scholar 

  3. M. Deza, R.C. Mullin and S.A. Vanstone, "Room squares and equidistant permutation arrays", Ars Combinatoria 2 (1976), 235–244.

    MathSciNet  MATH  Google Scholar 

  4. 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.

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  6. John Riordan, An Introduction to Combinatorial Analysis, Wiley (1958).

    Google Scholar 

  7. S.A. Vanstone, "The asymptotic behaviour of equidistant permutation arrays", submitted to Canad. J. Math.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/BFb0062526

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive