Polynomials, meanders, and paths in the lattice of noncrossing partitions

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n-1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n - 1 singular fibres. In this case, the topology of C(f) is determined by the data of an n-tuple of noncrossing matchings on the set {0,1,..., 2n - 1} with certain extra properties. We prove that there are 2(2n)n-2 such n-tuples, and that all of them arise from the topology of C(f) for some polynomial f.

Original languageEnglish (US)
Pages (from-to)3083-3107
Number of pages25
JournalTransactions of the American Mathematical Society
Volume361
Issue number6
DOIs
StatePublished - Jun 2009

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Noncrossing Partitions
Topology
Polynomials
Path
Polynomial
Fiber
n-tuple
Fibers
Algebraic curve
Circle
Harmonic
Roots

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Polynomials, meanders, and paths in the lattice of noncrossing partitions. / Savitt, David L.

In: Transactions of the American Mathematical Society, Vol. 361, No. 6, 06.2009, p. 3083-3107.

Research output: Contribution to journalArticle

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