The vertices of simplicial complexes are usually totally ordered so that face maps of each simplex can be defined easily for the purposes of homology. That gives an "oriented" simplicial complex.

But that's not always necessary, since a partial order that restricts to a total order on each simplex would also suffice. In fact, that is called an "ordered" simplicial complex.

One could generalize this even more to consider irreflexive binary relations that restrict to a total order on each simplex; as a consequence these relations will also be antisymmetric. Is there a name for such relations?

(Cross posted to Math Overflow)

  • $\begingroup$ Migrating a question means that it literally moves to another site. You can't quite do that yourself, you can ask a moderator to migrate this (e.g. via raising a flag asking for the question to be migrated). What you did was to cross post the question on MathOverflow. $\endgroup$ – Asaf Karagila Mar 3 '16 at 13:50

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