Basics of DTS quasigroups: Algebra, geometry and enumeration

Abstract

A directed triple system can be defined as a decomposition of a complete digraph to directed triples 〈x, y, z〉. By setting xy = z, yz = x, xz = y and uu = u we get a binary operation that can be a quasigroup. We give an algebraic description of such quasigroups, explain how they can be associated with triangulated pseudosurfaces and report enumeration results.