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IMA Journal of Mathematical Control and Information 1986 3(2-3):137-150; doi:10.1093/imamci/3.2-3.137
© 1986 by Institute of Mathematics and its Applications
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Towards a Cell Decomposition for Rational Functions

P. A. FUHRMANN and P. S. KRISHNAPRASAD

Department of Mathematics, Ben Gurion University of the Negev Beer-Sheva, Israel
Department of Electrical Engineering, University of Maryland College Park, MD 20742, USA

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.


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