ON THE COMBINATORICS OF POLYNOMIAL GENERALIZATIONS OF ROGERS-RAMANUJAN TYPE IDENTITIES

Print ISSN: 0972-7752

Abstract

In this paper following some ideas introduced by Andrews (Combinatorics and Ramanujan’s “lost” notebook, London Mathematical Society Lecture Note Series, No. 103, Cambridge University Press, London, 1985, pp. 1-23) and results given by Santos (Computer algebra and identities of the Rogers- Ramanujan type. Ph.D. Thesis, Pennsylvania State University, 1991) we give a polynomial generalization for the Fibonacci sequence from which we get new formula and combinatorial interpretation for the Fibonacci Numbers. c 2002 Elsevier Science B.V. All rights reserved.

Keywords and Phrases

Rogers-Ramanujan type identities, Fibonacci numbers, partitions.

A.M.S. subject classification

33D15, 05A17, 05A30, 11P81.

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