论文标题
开放格言步行的代数区域枚举
Algebraic area enumeration for open lattice walks
论文作者
论文摘要
我们通过用于枚举封闭步行的操作员方法的扩展，计算正方形平面晶格上固定长度和代数区域的开放步行数量。开放的步行区域是通过在其端点上的直线关闭行走来定义的，并且可以在晶格单元中假设半数。我们还得出了步行的长度和区域计数，并在特定的直线上具有端点，并概述了处理完全固定端点的步行方法的方法。
We calculate the number of open walks of fixed length and algebraic area on a square planar lattice by an extension of the operator method used for the enumeration of closed walks. The open walk area is defined by closing the walks with a straight line across their endpoints and can assume half-integer values in lattice cell units. We also derive the length and area counting of walks with endpoints on specific straight lines and outline an approach for dealing with walks with fully fixed endpoints.
