Polynomials, meanders, and paths in the lattice of noncrossing partitions
| dc.creator | Savitt, David | |
| dc.date | 2006-06-07 | |
| dc.date | 2007-09-27 | |
| dc.date.accessioned | 2026-07-07T08:32:26Z | |
| dc.date.available | 2026-07-07T08:32:26Z | |
| dc.description | 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. | |
| dc.description | 24 pages, 7 figures. To appear, Transactions of the A.M.S. Revised based on referee report; final section added | |
| dc.identifier | https://arxiv.org/abs/math/0606169 | |
| dc.identifier | http://arxiv.org/abs/math/0606169 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138794 | |
| dc.subject | Combinatorics | |
| dc.subject | 52C99, 05A18 | |
| dc.title | Polynomials, meanders, and paths in the lattice of noncrossing partitions | |
| dc.type | text |