Basics of DTS quasigroups: algebra, geometry and enumeration

Aleš Drápal; Terry S. Griggs; Andrew R. Kozlik

doi:10.1142/S0219498815500899

Basics of DTS quasigroups: algebra, geometry and enumeration

Combinatorics 2026-08-01 v1

Authors: Aleš Drápal , Terry S. Griggs , Andrew R. Kozlik

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Abstract

A directed triple system can be defined as a decomposition of a complete digraph to directed triples $\langle x,y,z\rangle$ . 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.

Cite

@article{arxiv.2608.00532,
  title  = {Basics of DTS quasigroups: algebra, geometry and enumeration},
  author = {Aleš Drápal and Terry S. Griggs and Andrew R. Kozlik},
  journal= {arXiv preprint arXiv:2608.00532},
  year   = {2026}
}