Harmonic Algebraic Curves and Noncrossing Partitions

@article{Martin2007HarmonicAC,
title={Harmonic Algebraic Curves and Noncrossing Partitions},
author={Jeremy L. Martin and David Savitt and Thomas Singer},
journal={Discrete & Computational Geometry},
year={2007},
volume={37},
pages={267-286}
}

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