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

• 作者: Cecília Pereira de Andrade Elen Viviani Pereira da Silva José Plínio de Oliveira Santos Kênia Cristina Pereira Silva
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: PARTITIONS FIBONACCI NUMBERS Pell NUMBERS Jacobsthal NUMBERS Q-ANALOG
• 年，卷（期）: 2013,（1）
• 页码范围: 25-32
• 页数: 8页
• 分类号: O1

摘要

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].