论文标题
各向异性POTTS模型上的功能关系：从Biggs公式到四面体方程
Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation
论文作者
论文摘要
我们探索了多元Tutte多项式家庭的几种类型的功能关系：Biggs公式和Star-Triangle（$ Y-u-δ$）转换在关键点$ n = 2 $。我们推断出Matiyasevich的定理及其与Biggs公式的倒数，并应用此关系以在参数$ n $上构建递归。在$ n = 2 $多变量Tutte多项式中，我们提供了两种不同的证明Zamolodchikov四面体方程，该方程满足了星形三角形转换，我们将后者扩展到了Valency 2点，并显示了Biggs公式和Star-Triangle转换通勤。
We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle ($Y-Δ$) 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.
