完全支持Kasteleyn算子与二分环形图相关联
Full support of the Kasteleyn operator associated with a bipartite toroidal graph
摘要：
嵌入在环面上的二部图中的完美匹配定义了图的面上的高度函数和$\Z^2$中的关联高度变化向量。这些匹配通过二元Laurent多项式的四个评估的组合来枚举，称为Kasteleyn算子，其二次系数（i，j）是直到符号，具有高度变化的完美匹配的数量（i，j）。因此，Kasteleyn算子的牛顿多边形是高度变化向量的凸包。在这篇文章中，我们证明了任何点的整数坐标在该多边形是实现一个完美的匹配。
英文摘要：
A perfect matching in a bipartite graph embedded on a torus defines a height function on the graph's faces and an associated height change vector in $\Z^2$. These matchings are enumerated by a combination of four evaluations of a bivariate Laurent polynomial, called Kasteleyn operator, whose coefficient of bidegree (i,j) is, up to the sign, the number of perfect matchings with height change (i,j). Therefore the Newton polygon of the Kasteleyn operator is the convex hull of the height change vectors. In this article, we prove that any point with integer coordinates in that polygon is realized by a perfect matching.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
