Is there a commonly-used name for a complete preorder (a transitive and total relation, Sloan's A000670 and A011782 for labeled and unlabeled, respectively) within set theory? (Not a total order, mind you -- it need not be antisymmetric.) I've heard the term "weak order", but that's from the same field that uses "linear order" for total orders, so I wanted some clarification if anyone knows of something else.(adsbygoogle = window.adsbygoogle || []).push({});

Also, does anyone know about counting the number of elements in complete relations? Götz Pfeiffer has an excellent paper Counting Transitive Relations about counting transitive relations (mentioning 26 classes of relations along the way), but he doesn't touch on the slightly-more-manegable complete relations at all.

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# Complete preorders (and other binary relations)

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