Physical Sciences and Mathematics Commons^™

A Simplification Of Inclusion-Exclusion Via Minimal Complexes, Andrew J. Brandt

Summer Research

This poster discusses the discovery and use of previously unproved methods for solving counting problems using the fundamental ideas of the inclusion exclusion-principle and the Euler characteristic. While both methods use a weighted version of the Euler characteristic to determine the order of a union of finite sets, the first method can be used with contractible, planar graphs whereas the second method generalizes this idea to multi-dimensional complexes and their minimal complexes. These methods seem to be promising in their applications to subjects such as homology theory, Betti numbers, and abstract tubes.