Divisors and specializations of Lucas polynomials
Combinatorics
2014-09-16 v3
Abstract
Three-term recurrences have infused stupendous amount of research in a broad spectrum of the sciences, such as orthogonal polynomials (in special functions) and lattice paths (in enumerative combinatorics). Among these are the Lucas polynomials, which have seen a recent true revival. In this paper one of the themes of investigation is the specialization to the Pell and Delannoy numbers. The underpinning motivation comprises primarily of divisibility and symmetry. One of the most remarkable findings is a structural decomposition of the Lucas polynomials into what we term as flat and sharp analogs.
Keywords
Cite
@article{arxiv.1406.0432,
title = {Divisors and specializations of Lucas polynomials},
author = {Tewodros Amdeberhan and Mahir Bilen Can and Melanie Jensen},
journal= {arXiv preprint arXiv:1406.0432},
year = {2014}
}
Comments
Minor typos are fixed, new references are added. To appear in Journal of Combinatorics