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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


CiteScore 2017: 0.28

SCImago Journal Rank (SJR) 2017: 0.231
Source Normalized Impact per Paper (SNIP) 2017: 0.443

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2391-4661
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Volume 49, Issue 3

Issues

A Combinatorial Proof of a Result on Generalized Lucas Polynomials

Alexandre Laugier / Manjil P. Saikia
  • Corresponding author
  • DIPLOMA STUDENT, MATHEMATICS GROUP THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS 11, STRADA COSTIERA TRIESTE, ITALY
  • current address: FACULTY OF MATHEMATICS UNIVERSITY OF VIENNA OSKAR-MORGENSTERN-PLATZ 1 1090 WIEN, AUSTRIA
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Published Online: 2016-08-20 | DOI: https://doi.org/10.1515/dema-2016-0022

Abstract

We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.

Keywords: binomial theorem; Fibonacci number; Fibonomial coefficient; Lucas number q-analogue; Generalized Lucas Polynomials

References

  • [1] T. Amdeberhan, X. Chen, V. H. Moll, B. E. Sagan, Generalized Fibonacci polynomials and Fibonomial coefficients, Ann. Comb. 18(4) (2014), 541-562.Google Scholar

  • [2] S. Ekhad, The Sagan-Savage Lucas-Catalan polynomials have positive coefficients, preprint http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/bruce.html.Google Scholar

  • [3] B. E. Sagan, C. D. Savage, Combinatorial interpretations of binomial coefficient analogues related to Lucas sequences, Integers, A52, 10 (2010), 697-703.Google Scholar

About the article

Received: 2014-03-26

Published Online: 2016-08-20

Published in Print: 2016-09-01


Citation Information: Demonstratio Mathematica, Volume 49, Issue 3, Pages 266–270, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.1515/dema-2016-0022.

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© by Manjil P. Saikia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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