Jon Azose

Harvey Mudd College Mathematics 2007

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Thesis Proposal: Applications of q-Binomial Coefficients to Counting Problems
Final Report: Final Report!
Thesis Advisor: Prof. Arthur T. Benjamin
Second Reader: Prof. Kristina C. Garrett

Applications of q-Binomial Coefficients to Counting Problems

I have developed a tiling interpretation of the q-binomial coefficients. The aim of this thesis is to apply this combinatorial interpretation to a variety of q-identities to provide straightforward combinatorial proofs. The range of identities I present include q-multinomial identities, alternating sum identities and congruences.