Open Access Senior Thesis
Bachelor of Science
Arthur T. Benjamin
© 2010 Bo Chen
In 1961, Kasteleyn, Fisher, and Temperley gave a result for the number of possible tilings of a 2m 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.
Chen, Bo, "Combinatorial Proofs Using Complex Weights" (2010). HMC Senior Theses. 16.