ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES
A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincaré and naturally appear in various areas of mathematics, theoretical physics and computati...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2020-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508620000025/type/journal_article |
| Summary: | A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincaré and naturally appear in various areas of mathematics, theoretical physics and computational biology (in particular, they provide a model of polymer folding). Enumeration of meanders is an important open problem. The number of meanders with $2N$ crossings grows exponentially when $N$ grows, but the long-standing problem on the precise asymptotics is still out of reach. |
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| ISSN: | 2050-5086 |