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

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References

Publications referenced by this paper.
Showing 1-10 of 12 references

Walsh , Counting unrooted maps on the plane

  • Valery A. Liskovets, R. Timothy
  • The On - Line Encyclopedia of Integer Sequences
  • 2005

Viro, Patchworking algebraic curves disproves the Ragsdale conjecture

  • Ilia Itenberg, Oleg
  • Math. Intelligencer
  • 1996
1 Excerpt

Pairings of 2n points on a circle

  • R. W. Goldbach, R. Tijdeman
  • Utilitas Math. 38
  • 1990
1 Excerpt

Mathematics and Its History, Springer-Verlag

  • John Stillwell
  • New York,
  • 1989

Achievements in the topology of real algebraic varieties in the last six years

  • O.Ya. Viro
  • Russian Math. Surveys
  • 1986

Viro , Achievements in the topology of real algebraic varieties in the last six years , Russian Math

  • O. Ya.
  • Surveys
  • 1986

Gluing of plane real algebraic curves and constructions of curves of degrees 6 and 7, Topology (Leningrad

  • O.Ya. Viro
  • Lecture Notes in Math.,
  • 1982
1 Excerpt

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