Note: a permutation group determined by an ordered set

Authors:
Anders Claesson;Chris D. Godsil;David G. Wagner
Affiliations:
Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada N2L 3G1;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada N2L 3G1
Venue:
Discrete Mathematics
Year:
2003

Citing 2
Cited 1

Enumerative combinatorics

Enumerative combinatorics
Computational complexity

Handbook of combinatorics (vol. 2)

Commutativity conditions for groups arising from acyclic directed graphs and posets

European Journal of Combinatorics

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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.