# Bo Chen

## Thesis

Combinatorial Proofs Using Complex Weights

Arthur T. Benjamin
In 1961, Kasteleyn, Fisher, and Temperley gave a result for the number of possible tilings of a $2m \times 2n$ checkerboard with dominoes. Their proof involves the evaluation of a complicated Pfaffian. In this thesis we investigate combinatorial strategies to evaluate the sum of evenly spaced binomial coefficients, and present steps towards a purely combinatorial proof of the 1961 result.