A transfer matrix approach to the enumeration of colored links
| dc.creator | Jacobsen, Jesper | |
| dc.creator | Zinn-Justin, Paul | |
| dc.date | 2001-04-05 | |
| dc.date | 2001-09-03 | |
| dc.date.accessioned | 2026-07-07T04:28:23Z | |
| dc.date.available | 2026-07-07T04:28:23Z | |
| dc.description | We propose a transfer matrix algorithm for the enumeration of alternating link diagrams with external legs, giving a weight $n$ to each connected component. Considering more general tetravalent diagrams with self-intersections and tangencies allows us to treat topological (flype) equivalences. This is done by means of a finite renormalization scheme for an associated matrix model. We give results, expressed as polynomials in $n$, for the various generating functions up to order 19 (link diagrams), 15 (prime alternating tangles) and 11 (6-legged links) intersections. The limit $n\to\infty$ is solved explicitly. We then analyze the large-order asymptotics of the generating functions. For $0\le n \le 2$ good agreement is found with a conjecture for the critical exponent, based on the KPZ relation. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0104009 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0104009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56769 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Combinatorics | |
| dc.title | A transfer matrix approach to the enumeration of colored links | |
| dc.type | text |