Combinatorial Cellular Decompositions for the Space of Complex Coefficient Polynomials

Details Combinatorial Cellular Decompositions for the Space of Complex Coefficient Polynomials Combinatorial Cellular Decompositions for the Space of Complex Coefficient Polynomials

2009-01-26

arxiv.org/abs/0901.4030v3

Mathematics

Combinatorics

22 pages, 11 figures

Scientific paper

We describe a classification of degree n complex coefficient polynomials with respect to combinatorial patterns that arise from the two real algebraic curves obtained as the zero sets for their real and imaginary part. In particular, we work out explicitly this classification for degree 3 polynomials, and other special families of polynomials. This work extends to the singular case similar considerations of Martin, Savitt, and Singer for non-singular basketballs.

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