Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation
We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle ( − Δ) transformation at the critical point = 2. We deduce the theorem of Matiyasevich and its inverse from the Biggs formula, and we apply this relation to co...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211314 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation. Boris Bychkov, Anton Kazakov and Dmitry Talalaev. SIGMA 17 (2021), 035, 30 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle ( − Δ) transformation at the critical point = 2. We deduce the theorem of Matiyasevich and its inverse from the Biggs formula, and we apply this relation to construct the recursion on the parameter n. We provide two different proofs of the Zamolodchikov tetrahedron equation satisfied by the star-triangle transformation in the case of = 2 multivariate Tutte polynomial. We extend the latter to the case of valency 2 points and show that the Biggs formula and the star-triangle transformation commute.
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| ISSN: | 1815-0659 |