The Kashaev Equation and Related Recurrences
The Kashaev Equation and Related Recurrences
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卡沙耶夫方程和相关递归式
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
A. Leaf
中科院分区：
文献类型：
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作者：
A. Leaf
六面体递推是由R. Kenyon和R. Pemantle在统计力学的双二聚体模型研究中引入的。它描述了一个方阵的若干次阵之间的关系。这种递归式与Kashaev方程密切相关，Kashaev方程的根源在于Ising模型和对对称矩阵的主次关系式的研究。六面体递推式的某些解局限于Kashaev方程的解。我们刻画了Kashaev方程的解可以通过这样的限制得到。这一性质引出了关于对称矩阵的主次矩阵的新结果。我们描述和研究了其他与Kashaev方程和六面体递归相似的递归式。这些包括出现在s-全纯性研究中的方程，以及其他递归式，如六面体递归式，可以与簇代数相关。
The hexahedron recurrence was introduced by R. Kenyon and R. Pemantle in the study of the double-dimer model in statistical mechanics. It describes a relationship among certain minors of a square matrix. This recurrence is closely related to the Kashaev equation, which has its roots in the Ising model and in the study of relations among principal minors of a symmetric matrix. Certain solutions of the hexahedron recurrence restrict to solutions of the Kashaev equation. We characterize the solutions of the Kashaev equation that can be obtained by such a restriction. This characterization leads to new results about principal minors of symmetric matrices. We describe and study other recurrences whose behavior is similar to that of the Kashaev equation and hexahedron recurrence. These include equations that appear in the study of s-holomorphicity, as well as other recurrences which, like the hexahedron recurrence, can be related to cluster algebras.