Order

, Volume 19, Issue 2, pp 101–113 | Cite as

Partially Well-Ordered Closed Sets of Permutations

  • M. D. Atkinson
  • M. M. Murphy
  • N. Ruškuc
Article

Abstract

It is known that the “pattern containment” order on permutations is not a partial well-order. Nevertheless, many naturally defined subsets of permutations are partially well-ordered, in which case they have a strong finite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as to where the boundary between partially well-ordered and not partially well-ordered classes lies.

finite basis involvement partial well-order pattern containment permutation 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. D. Atkinson
    • 1
  • M. M. Murphy
    • 2
  • N. Ruškuc
    • 2
  1. 1.Department of Computer ScienceUniversity of OtagoNew Zealand
  2. 2.School of Mathematics and StatisticsUniversity of St AndrewsU.K.

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