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Bo Chen

Picture of Bo Chen.

Thesis

Combinatorial Proofs Using Complex Weights

Advisor
Arthur T. Benjamin
Second Reader(s)
Kimberly Tucker

Abstract

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.

Proposal

Domino Tilings on Checkerboards

Additional Materials

Poster