A permutation group determined by an ordered set

Anders Claesson*, Chris D. Godsil, David G. Wagner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Let P be a finite ordered set, and let J(P) be the distributive lattice of order ideals of P. The covering relations of J(P) are naturally associated with elements of P; in this way, each element of P defines an involution on the set J(P). Let Γ(P) be the permutation group generated by these involutions. We show that if P is connected then Γ(P) is either the alternating or the symmetric group. We also address the computational complexity of determining which case occurs.

Original languageEnglish
Pages (from-to)273-279
Number of pages7
JournalDiscrete Mathematics
Volume269
Issue number1-3
DOIs
Publication statusPublished - 28 Jul 2003

Bibliographical note

Funding Information:
Research supported by operating grants from the Natural Sciences and Engineering Research Council of Canada.

Other keywords

  • Distributive lattice
  • Ordered set
  • Permutation group

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