Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Bychkov, Boris, Kazakov, Anton, Talalaev, Dmitry
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211314
• 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

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 cons...