A permutation group determined by an ordered set

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

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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
Early online date21 May 2003
DOIs
Publication statusPublished - 28 Jul 2003

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Keywords

  • ordered set
  • distributive lattice
  • permutation group

Cite this

Claesson, A., Godsil, C. D., & Wagner, D. G. (2003). A permutation group determined by an ordered set. Discrete Mathematics, 269(1-3), 273–279. https://doi.org/10.1016/S0012-365X(03)00094-3