TITLE:
Polynomial Generalizations and Combinatorial Interpretations for Sequences Including the Fibonacci and Pell Numbers
AUTHORS:
Cecília Pereira de Andrade, José Plínio de Oliveira Santos, Elen Viviani Pereira da Silva, Kênia Cristina Pereira Silva
KEYWORDS:
Partitions; Fibonacci Numbers; Pell Numbers; Jacobsthal Numbers; q-Analog
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.3 No.1,
January
29,
2013
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].