A Combinatorial Proof of a Result on Generalized Lucas Polynomials

Demonstratio mathematica

article

Alexandre Laugier¹  Manjil P. Saikia² 

[1] LYCÉE TRISTAN CORBIÈRE;DIPLOMA STUDENT, MATHEMATICS GROUP THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL

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

DOI  :  10.1515/dema-2016-0022

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY