Sean Plott

Harvey Mudd College Mathematics 2008

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Thesis Proposal: Determinants in Pascal's Triangle
Final Thesis: Functions of the Binomial Coefficient
Thesis Advisor: Prof. Arthur T. Benjamin
Second Reader: Prof. Kimberly Tucker

Functions of the Binomial Coefficient

The well-known binomial coefficient is the building block of Pascal's triangle. We explore the effect of replacing each factor of the binomial coefficient with some function of that factor. For example, we could replace each factor with a triangular number or a Fibonacci number. Through examining these new mathematical objects, we provide proofs of connections between Catalan numbers, determinants, non-intersecting paths, Pascal-like triangles, and Baxter permutations.