The Kauffman Constraint Coefficients Kw
| Autor: | Griggs, Kenneth A. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The Kauffman Constraint Coefficients Kw and their corresponding Elementals Ew are presented as solutions to the construction of the (beta)-derivative of Kauffman's Theta-function. Additionally, a new recursion relation is provided to construct the (beta)-derivative of Theta that requires only operational substitutions and summations; this algorithmically simplifies Kauffman's original technique. To demonstrate Kw, we generate the 30 Kw Coefficients from the corresponding Elementals Ew for the (9)-derivative of Theta and find that our results are in complete agreement with Kauffman's Mathematica\texttrademark solutions. We further present a calculation of two coefficients for the (12)-derivative of Theta and invite readers to use Mathematica\texttrademark or any other means to calculate and verify our results. Finally, we present a challenging calculation for a coefficient of the (40)-derivative of Theta; owing to the vast numbers of permutations involved, a Mathematica\texttrademark approach may require substantial computer resources to obtain the solution in a reasonable time. Comment: 8 pages, 8 sections, 2 Tables |
| Databáze: | arXiv |
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