| Autor: |
Bychkov, Boris, Kazakov, Anton, Talalaev, Dmitry |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
SIGMA 17 (2021), 035, 30 pages |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.3842/SIGMA.2021.035 |
| Popis: |
We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle ($Y-\Delta$) transformation at the critical point $n=2$. 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 $n=2$ 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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