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| Authors: | Johann?Cigler author-information" > author-information__contact u-icon-before" > mailto:johann.cigler@univie.ac.at" title=" johann.cigler@univie.ac.at" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | (1) Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090 Wien, Austria |
| Abstract: | We derive some formulas for the Carlitz q-Fibonacci polynomials Fn(t) which reduce to the finite version of the Rogers-Ramanujan identities obtained by I. Schur for t = 1. Our starting point is a representation of the q-Fibonacci polynomials as the weight of certain lattice paths in contained in a strip along the x-axis. We give an elementary combinatorial proof by using only the principle of inclusion-exclusion and some standard facts from q-analysis. |
| Keywords: | 05A19 05A30 11B39 11B65 11P81 |
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