11. A cyclic order is required to be symmetric under cyclic permutation,, and asymmetric under reversal :. 12. A ternary relation is called a cyclic order if it is cyclic, asymmetric, transitive, and total. 13. A separation relation is a quaternary relation that can be thought of as a cyclic order without an orientation. 14. In the standard link diagram, the Borromean rings are ordered non-transitively, in a cyclic order . 15. The 3 ! / 3 = 2 things you counted are 012 and 210 ( as cyclic orders ). 16. Instead, a cyclic order is defined as a ternary relation, meaning " after, one reaches before ". 17. An embedded graph also defines natural cyclic orders of edges which constitutes the boundaries of the faces of the embedding. 18. The relationship between partial and total cyclic orders is more complex than the relationship between partial and total linear orders. 19. A cyclic order on a set can be determined by a linear order on, but not in a unique way. 20. In this way it is a final, further weakening of the concepts of a betweenness relation and a cyclic order .
