Rational Convolution Roots of Isobaric Polynomials

Autor:	Conci, Aura, Li, Huilan, MacHenry, Trueman
Rok vydání:	2014
Předmět:	Mathematics - Number Theory Primary 11B39 Secondary 11B75 11N99 05E05
Druh dokumentu:	Working Paper
Popis:	In this paper, we exhibit two matrix representations of the rational roots of generalized Fibonacci polynomials (GFPs) under convolution product, in terms of determinants and permanents, respectively. The underlying root formulas for GFPs and for weighted isobaric polynomials (WIPs), which appeared in an earlier paper by MacHenry and Tudose, make use of two types of operators. These operators are derived from the generating functions for Stirling numbers of the first kind and second kind. Hence we call them Stirling operators. To construct matrix representations of the roots of GFPs, we use the Stirling operators of the first kind. We give explicit examples to show how the Stirling operators of the second kind appear in the low degree cases for the WIP-roots. As a consequence of the matrix construction, we have matrix representations of multiplicative arithmetic functions under the Dirichlet product into its divisible closure. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1404.5224 Zobrazit plný text záznamu View this record from Arxiv