## The number of convex topologies on a finite totally ordered set.(English)Zbl 1309.05019

Summary: We give an algorithm to find the number $$T_{\mathrm{cvx}}(n)$$ of convex topologies on a totally ordered set $$X$$ with $$n$$ elements, and present these numbers for $$n \leq 10$$.

### MSC:

 05A15 Exact enumeration problems, generating functions 06F30 Ordered topological structures 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

### Keywords:

convex topology; totally ordered set; number of topologies

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