A permutation group determined by an ordered set

Claesson, Anders and Godsil, Chris D. and Wagner, David G. (2003) A permutation group determined by an ordered set. Discrete Mathematics, 269 (1-3). 273–279. ISSN 0012-365X (https://doi.org/10.1016/S0012-365X(03)00094-3)

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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.