The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links
Mathematical Physics
2009-11-07 v1 Combinatorics
math.MP
Abstract
The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding ``renormalization equations'' are derived. Some particular cases are studied in detail and solved exactly.
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Cite
@article{arxiv.math-ph/0106005,
title = {The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links},
author = {P. Zinn-Justin},
journal= {arXiv preprint arXiv:math-ph/0106005},
year = {2009}
}
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21 pages