图的凝聚、重叠Pfrons和匹配的叠加
Graphical condensation, overlapping Pfaffians and superpositions of matchings
摘要：
本文的目的是清楚地表明郭、严、叶和张的“图凝聚”恒等式是如何通过Kasteleyn-Percus匹配计数方法从经典的Pfidian恒等式得到的。克努特把相关的恒等式称为“重叠的普夫特恒等式”，并把证明的关键概念称为“匹配的叠加”。在我们统一介绍的材料，我们也给了一个显然未发表的一般“重叠Pfatthalan”身份的Krattenthaler。本文的前一个版本包含了Kasteleyn-Percus方法的错误应用，现在已得到纠正。
英文摘要：
The purpose of this note is to exhibit clearly how the "graphical condensation" identities of Kuo, Yan, Yeh and Zhang follow from classical Pfaffian identities by the Kasteleyn-Percus method for the enumeration of matchings. Knuth termed the relevant identities "overlapping Pfaffian" identities and the key concept of proof "superpositions of matchings". In our uniform presentation of the material, we also give an apparently unpublished general "overlapping Pfaffian" identity of Krattenthaler. A previous version of this paper contained an erroneous application of the Kasteleyn-Percus method, which is now corrected.
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。
