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Uniformly Scattered Factors

  • Lucian Ilie
  • Ion Petre
  • Grzegorz Rozenberg
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Abstract

A word u appears as a factor of another word v as it is: in one piece. When u is a subword of v, u may be scattered as several factors. We consider the case in between and put some restrictions on the number of factors as to which u is allowed to be scattered. A large class of partial orders which are generalizations of factors and subwords is obtained. Investigating the borderline between their finite and infinite antichains, we are able to fully characterize the property of being well partial order. The result generalizes Higman’s theorem.

Keywords

Partial Order Maximal Element Infinite Chain Empty Word Short Word 
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.

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References

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    G. Higman, Ordering by divisibility in abstract algebras, Proc. London Math. Soc., 2 (3) (1952), 326–336.MathSciNetMATHCrossRefGoogle Scholar
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    L. Ilie, Generalized factors of words, Fundamenta Inform., 33 (1998), 239–247.MathSciNetMATHGoogle Scholar
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    C. Nash-Williams, On well quasi-ordering finite trees, Proc. Cambridge Philos. Soc., 59 (1963), 833–835.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2000

Authors and Affiliations

  • Lucian Ilie
    • 1
  • Ion Petre
    • 2
  • Grzegorz Rozenberg
    • 3
    • 4
  1. 1.Turku Centre for Computer Science (TUCS)TurkuFinland
  2. 2.Turku Centre for Computer Science (TUCS) and Department of MathematicsUniversity of TurkuTurkuFinland
  3. 3.Department of Computer ScienceLeiden UniversityLeidenThe Netherlands
  4. 4.Department of Computer ScienceUniversity of Colorado at BoulderBoulderUSA

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