Journal of Combinatorics

Volume 6 (2015)

Number 1–2

Divisors and specializations of Lucas polynomials

Pages: 69 – 89

DOI: http://dx.doi.org/10.4310/JOC.2015.v6.n1.a5

Authors

Tewodros Amdeberhan (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Mahir Bilen Can (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Melanie Jensen (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Abstract

Three-term recurrences have infused a 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

Lucas polynomials, flat and sharp lucanomials, divisors, Iwahori-Hecke algebra

2010 Mathematics Subject Classification

05A10, 11B39

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