Western Kentucky University
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.