## Western Kentucky University

#### Poster Title

Fibonacci Numbers and Collections of Mutually Disjoint Convex Subsets of a Totally Ordered Set

#### Institution

Western Kentucky University

#### Faculty Advisor/ Mentor

Tom Richmond

#### Abstract

We present a combinatorial proof of an identity for the odd Fibonacci numbers F(2n+1) by counting the number of collections of mutually disjoint convex subsets of a totally ordered set of n points. We discuss how the problem is motivated by counting certain topologies on finite sets, and relate it to Pascal's triangle.

Fibonacci Numbers and Collections of Mutually Disjoint Convex Subsets of a Totally Ordered Set

We present a combinatorial proof of an identity for the odd Fibonacci numbers F(2n+1) by counting the number of collections of mutually disjoint convex subsets of a totally ordered set of n points. We discuss how the problem is motivated by counting certain topologies on finite sets, and relate it to Pascal's triangle.