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论文类型：期刊论文

发表时间：2014-12-01

发表刊物：ANNALS OF COMBINATORICS

收录刊物：SCIE

卷号：18

期号：4

页面范围：541-562

ISSN号：0218-0006

关键字：binomial theorem; Catalan number; Dodgson condensation; Euler-Cassini identity; Fibonacci number; Fibonomial coefficient; Lucas number q-analogue; valuation

摘要：The focus of this paper is the study of generalized Fibonacci polynomials and Fibonomial coefficients. The former are polynomials in variables s,t given by , and for . The latter are defined by where . These quotients are also polynomials in s, t and specializations give the ordinary binomial coefficients, the Fibonomial coefficients, and the q-binomial coefficients. We present some of their fundamental properties, including a more general recursion for , an analogue of the binomial theorem, a new proof of the Euler- Cassini identity in this setting with applications to estimation of tails of series, and valuations when s and t take on integral values. We also study a corresponding analogue of the Catalan numbers. Conjectures and open problems are scattered throughout the paper.