Summary: Let \(D_ n\) be the complete digraph on n nodes, and let \(P^ n_{LO}\) denote the convex hull of all incidence vectors of arc sets of linear orderings of the nodes of \(D_ n\) (i.e. these are exactly the acyclic tournaments of \(D_ n)\). We show that various classes of inequalities define facets of \(P^ n_{LO}\), e.g. the 3-dicycle inequalities, the simple k-fence inequalities and various Möbius ladder inequalities, and we discuss the use of these inequalities in cutting plane approaches to the triangulation problem of input-output matrices, i.e. the solution of permutation resp. linear ordering problems.

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.