Combinatorialization of Sury and McLaughlin identities, general linear recurrences in a unified approach
Combinatorics
2020-09-15 v1
Abstract
In this article we provide with combinatorial proofs of some recent identities due to Sury and McLaughlin. We show that, the solution of a general linear recurrence with constant coefficients can be interpreted as a determinant of a matrix. Also, we derive a determinantal expression of Fibonacci and Lucas numbers. We prove Binets formula for Fibonacci and Lucas numbers in a purely combinatorial way and in course of doing so, we find a determinantal identity, which we think to be new.
Keywords
Cite
@article{arxiv.2009.06162,
title = {Combinatorialization of Sury and McLaughlin identities, general linear recurrences in a unified approach},
author = {Sudip Bera},
journal= {arXiv preprint arXiv:2009.06162},
year = {2020}
}
Comments
16 pages, 11 figures