Combinatorial Proofs Using Complex Weights

Author

Bo Chen, Harvey Mudd CollegeFollow

Graduation Year

2010

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Arthur T. Benjamin

Reader 2

Kimberly Tucker

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2010 Bo Chen

Abstract

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.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/stc,330

Recommended Citation

Chen, Bo, "Combinatorial Proofs Using Complex Weights" (2010). HMC Senior Theses. 16.
https://scholarship.claremont.edu/hmc_theses/16