# The asymptotic number of prime alternating links

1 ADAGE - Applying discrete algorithms to genomics
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The first precise asymptotic result in enumerative knot theory is the determination by Sundberg and Thistlethwaite (\emph{Pac.\ J.\ Math.}, 1998) of the growth rate of the number $A_n$ of prime alternating links with $n$ crossings. They found $\lambda$ and positive constants $c_1$, $c_2$ such that $c_1 n^{-7/2}\lambda^n \leq A_n \leq c_2 n^{-5/2}\lambda^n.$ In this extended abstract, we prove that the asymptotic behavior of $A_n$ is in fact $A_n\; \mathop{\sim}_{n\rightarrow\infty} \;c_3\; n^{-7/2}\lambda^n,$ where $c_3$ is a constant with an explicit expression.
Mots-clés :
Type de document :
Communication dans un congrès
Barcelo, H. and Welker, V. Formal Power Series and Algebraic Combinatorics - FPSAC'2001, 2001, Phoenix, Arizona, Arizona State University, 10 p, 2001
Domaine :

https://hal.inria.fr/inria-00108015
Contributeur : Publications Loria <>
Soumis le : jeudi 19 octobre 2006 - 15:13:03
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48

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• HAL Id : inria-00108015, version 1

### Citation

Sébastien Kunz-Jacques, Gilles Schaeffer. The asymptotic number of prime alternating links. Barcelo, H. and Welker, V. Formal Power Series and Algebraic Combinatorics - FPSAC'2001, 2001, Phoenix, Arizona, Arizona State University, 10 p, 2001. 〈inria-00108015〉

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