A quantum combinatorial approach for computing a tetrahedral network of Jones-Wenzl projectors

2013/01/09 by Claire Levaillant, Claire Isabelle Levaillant, Levaillant, Claire Isabelle · 1 citation
Mathematics · #05E15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.CO #math.QA #msc:05E15

paper · pdf · doi:10.48550/arxiv.1301.1733

25 pages, 17 figures

arxiv created 2013/01/09 · openalex publication_date 2013/01/09 · arxiv updated 2013/01/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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