Fibonacci numbers and the Rogers-Ramanujan identities

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Abstract

In my research on the theory of partitions and related questions, I have often used recurrent integer sequences such as the Fibonacci numbers to obtain hints about the behavior of certain partition generating functions. In this article, I will illustrate this process by studying the relationship between the Fibonacci numbers and a sequence of polynomials used by Schur in his second proof of the Rogers-Ramanujan identities. I will try to make clear how generating function proofs of Fibonacci identities lead to analogous results for Schur's polynomials. We shall find that this approach helps explain why the generalization of Fibonacci formulas to Schur's polynomial is sometimes rather intricate.

Original languageEnglish (US)
Pages (from-to)3-19
Number of pages17
JournalFibonacci Quarterly
Volume42
Issue number1
StatePublished - Feb 1 2004

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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