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Physical Sciences and Mathematics Commons

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Mathematics

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Claremont Colleges

2020

05A19

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Full-Text Articles in Physical Sciences and Mathematics

An Exploration Of Combinatorial Interpretations For Fibonomial Coefficients, Richard Shapley Jan 2020

An Exploration Of Combinatorial Interpretations For Fibonomial Coefficients, Richard Shapley

HMC Senior Theses

We can define Fibonomial coefficients as an analogue to binomial coefficients as F(n,k) = FnFn-1 … F­n-k+1 / F­kFk-­1…F1, where Fn represents the nth Fibonacci number. Like binomial coefficients, there are many identities for Fibonomial coefficients that have been proven algebraically. However, most of these identities have eluded combinatorial proofs.

Sagan and Savage (2010) first presented a combinatorial interpretation for these Fibonomial coefficients. More recently, Bennett et al. (2018) provided yet another interpretation, that is perhaps more tractable. However, there still has been little progress towards using these interpretations …