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Harmonic algebraic curves and noncrossing partitions
dc.contributor.author | Martin, Jeremy L. | |
dc.contributor.author | Savitt, David | |
dc.contributor.author | Singer, Ted | |
dc.date.accessioned | 2010-06-17T20:55:04Z | |
dc.date.available | 2010-06-17T20:55:04Z | |
dc.date.issued | 2007-02 | |
dc.identifier.citation | Harmonic algebraic curves and noncrossing partitions (with David Savitt and Ted Singer), Discrete and Computational Geometry 37, no. 2 (2007), 267--286. | |
dc.identifier.uri | http://hdl.handle.net/1808/6355 | |
dc.description | This is the author's accepted manuscript. | |
dc.description.abstract | 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. | |
dc.publisher | Springer Verlag | |
dc.relation.hasversion | http://arxiv.org/abs/math.GR/0508630 | |
dc.title | Harmonic algebraic curves and noncrossing partitions | |
dc.type | Article | |
kusw.kuauthor | Martin, Jeremy L. | |
kusw.kudepartment | Mathematics | |
kusw.oastatus | fullparticipation | |
dc.identifier.doi | 10.1007/s00454-006-1283-6 | |
kusw.oaversion | Scholarly/refereed, author accepted manuscript | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess |