Brick图（不含非平凡紧割的非二部图）的Pfaffian定向问题是一个公开的问题。本项目研究brick图的Pfaffian定向及其相关问题，着重研究组合学领域中备受关注的solid brick图和正则brick图的Pfaffian定向问题，并利用图的Pfaffian定向理论研究六角网格图等Archimedean网格图的完美匹配计数问题。本项目期望通过找出solid brick图和正则brick图的递归构造规律和能识别其Pfaffian性的多项式算法，从而刻画它们的Pfaffian性。本项目的预期成果将为研究brick图的Pfaffian定向问题提供思想方法，进一步发展匹配理论。此外，本项目的研究具有学科交叉的性质和广泛的应用背景。

The Pfaffian orientation problem of brick is an open problem. In this project, we focus on Pfaffian orientation of bricks and related problems. We focus on recognizing Pfaffian solid brick and Pfaffian regular brick, counting the number of perfect matchings of honeycomb lattice and some other Archimedean lattices by Pfaffians. In this project, we hope to find the generating theorems of solid brick and regular brick, and polynomial algorithms that can recognize Pfaffifian bricks, so as to characterize their Pfaffian properties. The expected results of this project will provide ideas and methods for studying the Pfaffian orientation problem of bricks and promote the development of matching theory. In addition, the research of this project has the nature of interdisciplinary and a wide range of applications.