# Sean Plott

Harvey Mudd College Mathematics 2008

Thesis Proposal: | Determinants in Pascal's Triangle |
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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.