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

Clark, Tyler; Richmond, Tom

Involve 8, No. 1, 25-32 (2015).

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

Software:

OEIS