Towards a cell decomposition for rational functions

P. A. Fuhrmann; P. S. Krishnaprasad

doi:10.1093/imamci/3.2-3.137

Towards a cell decomposition for rational functions

P. A. Fuhrmann
, P. S. Krishnaprasad

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper, we investigate a decomposition of the space of reduced rational functions of fixed degree into continued fraction cells. We give a variety of combinatorial formulas pertaining to this decomposition and investigate the effect of certain scalings on the decomposition. We conjecture that the continued fraction decomposition is indeed a cell decomposition in the topological sense. We provide evidence in low dimensions for this to be true.

Original language	English
Pages (from-to)	137-150
Number of pages	14
Journal	IMA Journal of Mathematical Control and Information
Volume	3
Issue number	2-3
DOIs	https://doi.org/10.1093/imamci/3.2-3.137
State	Published - 1 Dec 1986

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Applied Mathematics

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10.1093/imamci/3.2-3.137

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AU - Krishnaprasad, P. S.

PY - 1986/12/1

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N2 - In this paper, we investigate a decomposition of the space of reduced rational functions of fixed degree into continued fraction cells. We give a variety of combinatorial formulas pertaining to this decomposition and investigate the effect of certain scalings on the decomposition. We conjecture that the continued fraction decomposition is indeed a cell decomposition in the topological sense. We provide evidence in low dimensions for this to be true.

AB - In this paper, we investigate a decomposition of the space of reduced rational functions of fixed degree into continued fraction cells. We give a variety of combinatorial formulas pertaining to this decomposition and investigate the effect of certain scalings on the decomposition. We conjecture that the continued fraction decomposition is indeed a cell decomposition in the topological sense. We provide evidence in low dimensions for this to be true.

UR - https://www.scopus.com/pages/publications/34447519675

U2 - 10.1093/imamci/3.2-3.137

DO - 10.1093/imamci/3.2-3.137

M3 - Article

AN - SCOPUS:34447519675

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VL - 3

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EP - 150

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

IS - 2-3

ER -

Towards a cell decomposition for rational functions

Abstract

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