Linear Recurrences and Power Series Division

Christoph Koutschan; Herwig Hauser

Linear Recurrences and Power Series Division

Christoph Koutschan, Herwig Hauser

Research Institute for Symbolic Computation

Research output: Working paper and reports › Research report

Abstract

Bousquet-Melou and Petkovsek investigated the generating functions of multivariate linear recurrences with constant coefficients. We will give a reinterpretation of their theory by means of division theorems for formal power series, which clarifies the structural background and provides short, conceptual proofs. In addition, extending the division to the context of differential operators, the case of recurrences with polynomial coefficients can be treated in an analogous way.

Original language	English
Place of Publication	University of Linz, Altenbergerstraße 69, 4040 Linz, Austria
Publisher	SFB F013
Number of pages	8
Publication status	Published - 2007

Publication series

Name	SFB F013 Reports
No.	2007-20

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Cite this

@techreport{528f3fe3ac0f4fa6b071b228abb9a094,

title = "Linear Recurrences and Power Series Division",

abstract = "Bousquet-Melou and Petkovsek investigated the generating functions of multivariate linear recurrences with constant coefficients. We will give a reinterpretation of their theory by means of division theorems for formal power series, which clarifies the structural background and provides short, conceptual proofs. In addition, extending the division to the context of differential operators, the case of recurrences with polynomial coefficients can be treated in an analogous way.",

author = "Christoph Koutschan and Herwig Hauser",

year = "2007",

language = "English",

series = "SFB F013 Reports",

publisher = "SFB F013",

number = "2007-20",

type = "WorkingPaper",

institution = "SFB F013",

}

TY - UNPB

T1 - Linear Recurrences and Power Series Division

AU - Koutschan, Christoph

AU - Hauser, Herwig

PY - 2007

Y1 - 2007

N2 - Bousquet-Melou and Petkovsek investigated the generating functions of multivariate linear recurrences with constant coefficients. We will give a reinterpretation of their theory by means of division theorems for formal power series, which clarifies the structural background and provides short, conceptual proofs. In addition, extending the division to the context of differential operators, the case of recurrences with polynomial coefficients can be treated in an analogous way.

AB - Bousquet-Melou and Petkovsek investigated the generating functions of multivariate linear recurrences with constant coefficients. We will give a reinterpretation of their theory by means of division theorems for formal power series, which clarifies the structural background and provides short, conceptual proofs. In addition, extending the division to the context of differential operators, the case of recurrences with polynomial coefficients can be treated in an analogous way.

M3 - Research report

T3 - SFB F013 Reports

BT - Linear Recurrences and Power Series Division

PB - SFB F013

CY - University of Linz, Altenbergerstraße 69, 4040 Linz, Austria

ER -