The number of convex topologies on a finite totally ordered set

The Number of Convex Topologies on a Finite Totally Ordered Set

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. 2010 Mathematics Subject Classification: 54A10, 54F05, 06F30, 05A15.

Semi-t-operators on a finite totally ordered set

Order-compatible Topologies on a Partially Ordered Set

Stirling number of the fourth kind and lucky partitions of a finite set

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

On the Number of Open Sets of Finite Topologies

Recent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points which is not discrete contains <(3/4)2” open sets, and that this inequality is best possible. We use the correspondence between finite TO-topologies and partial orders to find all non-homeomorphic topologies with n points and >(7/16)2” open sets. We determine which of these topologies are TO, and in the...