### Abstract

Language | English |
---|---|

Pages | 273–279 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 269 |

Issue number | 1-3 |

Early online date | 21 May 2003 |

DOIs | |

Publication status | Published - 28 Jul 2003 |

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### Keywords

- ordered set
- distributive lattice
- permutation group

### Cite this

*Discrete Mathematics*,

*269*(1-3), 273–279. https://doi.org/10.1016/S0012-365X(03)00094-3

}

*Discrete Mathematics*, vol. 269, no. 1-3, pp. 273–279. https://doi.org/10.1016/S0012-365X(03)00094-3

**A permutation group determined by an ordered set.** / Claesson, Anders; Godsil, Chris D.; Wagner, David G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A permutation group determined by an ordered set

AU - Claesson, Anders

AU - Godsil, Chris D.

AU - Wagner, David G.

PY - 2003/7/28

Y1 - 2003/7/28

N2 - 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.

AB - 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.

KW - ordered set

KW - distributive lattice

KW - permutation group

U2 - 10.1016/S0012-365X(03)00094-3

DO - 10.1016/S0012-365X(03)00094-3

M3 - Article

VL - 269

SP - 273

EP - 279

JO - Discrete Mathematics

T2 - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -