Harmonic Algebraic Curves and Noncrossing Partitions

  title={Harmonic Algebraic Curves and Noncrossing Partitions},
  author={Jeremy L. Martin and David Savitt and Thomas Singer},
  journal={Discrete & Computational Geometry},
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… CONTINUE READING

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