Harmonic algebraic curves and noncrossing partitions

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Issue Date
2007-02Author
Martin, Jeremy L.
Savitt, David
Singer, Ted
Publisher
Springer Verlag
Type
Article
Article Version
Scholarly/refereed, author accepted manuscript
Version
http://arxiv.org/abs/math.GR/0508630
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Show full item recordAbstract
Motivated by Gauss’s first proof of the fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a pair of noncrossing matchings satisfying one additional constraint. We prove that every noncrossing matching arises from some harmonic curve, and deduce from this that every basketball arises from some polynomial.
Description
This is the author's accepted manuscript.
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Citation
Harmonic algebraic curves and noncrossing partitions (with David Savitt and Ted Singer), Discrete and Computational Geometry 37, no. 2 (2007), 267--286.
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