The Combinatorics of Alternating Tangles: from theory to computerized enumeration
| dc.creator | Jacobsen, J. L. | |
| dc.creator | Zinn-Justin, P. | |
| dc.date | 2001-11-06 | |
| dc.date.accessioned | 2026-07-07T04:28:44Z | |
| dc.date.available | 2026-07-07T04:28:44Z | |
| dc.description | We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating) knots. Using a finite renormalization scheme for an associated matrix model, we first reduce the task to that of enumerating planar tetravalent diagrams with two types of vertices (self-intersections and tangencies), where now the subtle issue of topological equivalences has been eliminated. The number of such diagrams with $p$ vertices scales as $12^p$ for $p\to\infty$. We next show how to efficiently enumerate these diagrams (in time $\sim 2.7^p$) by using a transfer matrix method. We give results for various generating functions up to 22 crossings. We then comment on their large-order asymptotic behavior. | |
| dc.description | proceedings European Summer School St-Petersburg 2001 | |
| dc.identifier | https://arxiv.org/abs/math-ph/0111011 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0111011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56903 | |
| dc.subject | Mathematical Physics | |
| dc.title | The Combinatorics of Alternating Tangles: from theory to computerized enumeration | |
| dc.type | text |