A quantum combinatorial approach for computing a tetrahedral network of Jones-Wenzl projectors
Quantum Algebra
2013-01-11 v1 Combinatorics
Abstract
Trivalent plane graphs are used in various areas of mathematics which relate for instance to the colored Jones polynomial, invariants of 3-manifolds and quantum computation. Their evaluation is based on computations in the Temperley-Lieb algebra and more specifically the Jones-Wenzl projectors. We use the work by Kauffman-Lins to present a quantum combinatorial approach for evaluating a tetrahedral net. On the way we recover two equivalent definitions for the unsigned Stirling numbers of the first kind and we provide an equality for the quantized factorial using these numbers.
Keywords
Cite
@article{arxiv.1301.1733,
title = {A quantum combinatorial approach for computing a tetrahedral network of Jones-Wenzl projectors},
author = {Claire Isabelle Levaillant},
journal= {arXiv preprint arXiv:1301.1733},
year = {2013}
}
Comments
25 pages, 17 figures