Mathematics Commons^™

An Alternate Approach To Alternating Sums: A Method To Die For, Arthur T. Benjamin, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

The 99th Fibonacci Identity, Arthur T. Benjamin, Alex K. Eustis '06, Sean S. Plott '08

All HMC Faculty Publications and Research

We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left open in the book Proofs That Really Count [1], and generalize these to Gibonacci sequences G_n that satisfy the Fibonacci recurrence, but with arbitrary real initial conditions. We offer several new identities as well.

[1] A. T. Benjamin and J. J. Quinn, Proofs That Really Count: The Art of Combinatorial Proof, The Dolciani Mathematical Expositions, 27, Mathematical Association of America, Washington, DC, 2003

Paint It Black -- A Combinatorial Yawp, Arthur T. Benjamin, Jennifer J. Quinn, James A. Sellers, Mark A. Shattuck

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No abstract provided in this paper.

A Combinatorial Approach To Fibonomial Coefficients, Arthur T. Benjamin, Sean S. Plott '08

All HMC Faculty Publications and Research

A combinatorial argument is used to explain the integrality of Fibonomial coefficients and their generalizations. The numerator of the Fibonomial coeffcient counts tilings of staggered lengths, which can be decomposed into a sum of integers, such that each integer is a multiple of the denominator of the Fibonomial coeffcient. By colorizing this argument, we can extend this result from Fibonacci numbers to arbitrary Lucas sequences.