Vol. 8, No. 1, 2015

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The number of convex topologies on a finite totally ordered set

Tyler Clark and Tom Richmond

Vol. 8 (2015), No. 1, 25–32
Abstract

We give an algorithm to find the number Tcvx(n) of convex topologies on a totally ordered set X with n elements, and present these numbers for n 10.

Keywords
convex topology, totally ordered set, number of topologies
Mathematical Subject Classification 2010
Primary: 05A15, 06F30, 54A10, 54F05
Milestones
Received: 19 October 2011
Revised: 14 June 2013
Accepted: 7 August 2013
Published: 10 December 2014

Communicated by Kenneth S. Berenhaut
Authors
Tyler Clark
Department of Mathematics
Western Kentucky University
1906 College Heights Boulevard
Bowling Green, KY 42101
United States
Tom Richmond
Department of Mathematics
Western Kentucky University
1906 College Heights Boulevard
Bowling Green, KY 42101
United States