A transfer matrix approach to the enumeration of colored links

dc.creatorJacobsen, Jesper
dc.creatorZinn-Justin, Paul
dc.date2001-04-05
dc.date2001-09-03
dc.date.accessioned2026-07-07T04:28:23Z
dc.date.available2026-07-07T04:28:23Z
dc.descriptionWe 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.description35 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0104009
dc.identifierhttp://arxiv.org/abs/math-ph/0104009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56769
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectCombinatorics
dc.titleA transfer matrix approach to the enumeration of colored links
dc.typetext

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