Trickle groups unify right-angled Artin/Coxeter groups, cactus groups, Thompson group F, and ordered quandle groups, and they all inherit a terminating and confluent rewriting system and a solution to the word problem.
Circular orderability and quandles
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abstract
In this paper, we introduce the notion of circular orderability for quandles. We show that the set all right (respectively left) circular orderings of a quandle is a compact topological space. We also show that the space of right (respectively left) orderings of a quandle embeds in its space of right (respectively left) circular orderings. Examples of quandles that are not left circularly orderable and examples of quandles that are neither left nor right circularly orderable are given.
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Trickle groups
Trickle groups unify right-angled Artin/Coxeter groups, cactus groups, Thompson group F, and ordered quandle groups, and they all inherit a terminating and confluent rewriting system and a solution to the word problem.