论文标题
完全对称的自相平面分区中的相关性
Correlations in totally symmetric self-complementary plane partitions
论文作者
论文摘要
完全对称的自我平衡平面分区（TSSCPPS）是具有最大可能对称性的盒装平面分区。我们将tsscpps的众所周知表示形式作为一个二聚体模型，该模型在具有自由边界的六角形的二十二个蜂窝图上，以表达它们作为非双色平面图家族的完美匹配。我们的主要结果是TSSCPPS的边缘形成了PFAFFIAN点过程，为此，我们为逆Kasteleyn矩阵提供了明确的公式。然后，使用这些相关性的初步分析来对TSSCPPS的极限形状在缩放限制限制中给出精确的猜想。
Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of a hexagon with free boundary to express them as perfect matchings of a family of non-bipartite planar graphs. Our main result is that the edges of the TSSCPPs form a Pfaffian point process, for which we give explicit formulas for the inverse Kasteleyn matrix. Preliminary analysis of these correlations are then used to give a precise conjecture for the limit shape of TSSCPPs in the scaling limit.
