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