Skip to main content

Geometric Sets of Permutations

  • Conference paper
Geometries and Groups
  • 160 Accesses

Abstract

There has been some interest recently in analogues of designs, codes and geometries, in the setting of the symmetric group. The geometries described here, called permutation geometries, are analogous to matroids, and belong to a linear diagram in which all strokes except the last are linear spaces, while the last consists of the rank 2 permutation geometries.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H.F. Blichfeldt, A theorem concerning the invariants of linear homogeneous groups, with some applications to substitution groups, Trans. Amer. Math. Soc. 5 (1904), 461–466.

    Article  MathSciNet  MATH  Google Scholar 

  2. F. Buekenhout, Diagrams for geometries and groups, J. Combinatorial Theory (A) 27 (1979), 121–151.

    Article  MathSciNet  MATH  Google Scholar 

  3. P.J. Cameron, M. Deza and P. Frankl, Sharp sets of permutations, to appear in J. Algebra.

    Google Scholar 

  4. P.J. Cameron and D.E. Taylor, Stirling numbers and affine equivalence, Ars. Comb. 20B (1985), 3–14.

    MathSciNet  Google Scholar 

  5. P. Delsarte, Bilinear forms over a finite field, with applications to coding theory, J. Combinatorial Theory (A), 25 (1978), 226–241.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Deza and M. Laurent, Squashed designs, to appear.

    Google Scholar 

  7. W. M Kantor, 2-transitive designs, “Combinatorics” ed. M. Hall Jr. and J.H. van Lint), 365–418, Math. Centre Tracts, Amsterdam, 1975.

    Google Scholar 

  8. W.M. Kantor, Homogeneous designs and geometric lattices, J. Combinatorial Theory (A) 38 (1985), 66–74.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Kiyota, An inequality for finite permutation groups, J. Combinatorial Theory (A) 27 (1979), 119.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Maund, Geometric groups, dissertation, Oxford 1986.

    Google Scholar 

  11. M.E. O’Nan, Sharply 2-transitive sets of permutations, Proc. Rutgers Group Theory Year 1983–1984 (ed. M. Aschbacher et al.), 63–67, Cambridge Univ. Press, Cambridge, 1985.

    Google Scholar 

  12. J. Tits, “Buildings of Spherical Type and Finite BN-Pairs”, Lecture Notes in Math. 386, Springer, Berlin, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 D. Reidel Publishing Company, Dordrecht, Holland

About this paper

Cite this paper

Cameron, P.J. (1988). Geometric Sets of Permutations. In: Aschbacher, M., Cohen, A.M., Kantor, W.M. (eds) Geometries and Groups. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4017-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4017-8_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8282-2

  • Online ISBN: 978-94-009-4017-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics