Polynomial Generalizations and Combinatorial Interpretations for Sequences Including the Fibonacci and Pell Numbers

José Plínio de Oliveira Santos,Elen Viviani Pereira da Silva,Kênia Cristina Pereira Silva,Cecília Pereira de Andrade

doi:10.4236/ojdm.2013.31006

Abstract

In this paper we present combinatorial interpretations and polynomials generalizations for sequences including the Fibonacci numbers, the Pell numbers and the Jacobsthal numbers in terms of partitions. It is important to mention that results of this nature were given by Santos and Ivkovic in two papers published on the Fibonacci Quarterly, Polynomial generalizations of the Pell sequence and the Fibonacci sequence [1] and Fibonacci Numbers and Partitions [2] , and one, by Santos, on Discrete Mathematics, On the Combinatorics of Polynomial generalizations of Rogers-Ramanujan Type Identities [3]. By these results one can see that from the q-series identities important combinatorial information can be obtained by a careful study of the two variable function introduced by Andrews in Combinatorics and Ramanujan's lost notebook [4].

Highlights

In this paper we present combinatorial interpretations and polynomials generalizations for sequences including the Fibonacci numbers, the Pell numbers and the Jacobsthal numbers in terms of partitions
It is important to mention that results of this nature were given by Santos and Ivkovic in two papers published on the Fibonacci Quarterly, Polynomial generalizations of the Pell sequence and the Fibonacci sequence [1] and Fibonacci Numbers and Partitions [2], and one, by Santos, on Discrete Mathematics, On the Combinatorics of Polynomial generalizations of Rogers-Ramanujan Type Identities [3]
In this paper following some ideas introduced by Andrews [4] and results given by Santos [5] we give polynomial generalizations and combinatorial interpretations for sequences, including Fibonacci numbers, the Pell numbers and the Jacobsthal numbers in terms of partitions

Summary

Introduction

In this paper following some ideas introduced by Andrews [4] and results given by Santos [5] we give polynomial generalizations and combinatorial interpretations for sequences, including Fibonacci numbers, the Pell numbers and the Jacobsthal numbers in terms of partitions. In this paper we present combinatorial interpretations and polynomials generalizations for sequences including the Fibonacci numbers, the Pell numbers and the Jacobsthal numbers in terms of partitions.

Results

Conclusion