Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Fibonacci Deteminants - A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn
Fibonacci Deteminants - A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn
Jennifer J. Quinn
In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.
Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn
Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn
Jennifer J. Quinn
In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.
The Fibonacci Numbers -- Exposed More Discretely, Arthur T. Benjamin, Jennifer J. Quinn
The Fibonacci Numbers -- Exposed More Discretely, Arthur T. Benjamin, Jennifer J. Quinn
Jennifer J. Quinn
No abstract provided in this article.
Random Approaches To Fibonacci Identities, Arthur T. Benjamin, Gregory M. Levin, Karl Mahlburg '01, Jennifer J. Quinn
Random Approaches To Fibonacci Identities, Arthur T. Benjamin, Gregory M. Levin, Karl Mahlburg '01, Jennifer J. Quinn
Jennifer J. Quinn
No abstract provided in this article.
Phased Tilings And Generalized Fibonacci Identities, Arthur T. Benjamin, Jennifer J. Quinn, Francis E. Su
Phased Tilings And Generalized Fibonacci Identities, Arthur T. Benjamin, Jennifer J. Quinn, Francis E. Su
Jennifer J. Quinn
Fibonacci numbers arise in the solution of many combinatorial problems. They count the number of binary sequences with no consecutive zeros, the number of sequences of 1's and 2's which sum to a given number, and the number of independent sets of a path graph. Similar interpretations exist for Lucas numbers. Using these interpretations, it is possible to provide combinatorial proofs that shed light on many interesting Fibonacci and Lucas identities (see [1], [3]). In this paper we extend the combinatorial approach to understand relationships among generalized Fibonacci numbers. Given G0 and G1 a generalized Fibonacci sequence G0, G1, G2,... …
Recounting Fibonacci And Lucas Identities, Arthur T. Benjamin, Jennifer J. Quinn
Recounting Fibonacci And Lucas Identities, Arthur T. Benjamin, Jennifer J. Quinn
Jennifer J. Quinn
No abstract provided in this article.