论文标题
通过非晶格路径获得的一定比例
A certain ratio of generating functions of lozenge tilings, obtained with non--intersecting lattice paths
论文作者
论文摘要
在最近的预印本中，LAI弄清楚了两个“半hexagons横向凹痕的半六角形”的加权润滑块的功能，这仅在宽度上有所不同。 LAI通过使用“图形凝结”（即将某些PFAFFIAN身份应用于匹配的加权枚举）实现了这一目标。 本说明的目的是展示如何通过Lindström-gessel- viennot方法来以一种非常简单的方式来降低晶格路径。基本上，相同的观察结果，但仅限于枚举（即，所有lozenge砖的权重等于$ 1 $），均包含在最近的Condon预印象中。
In a recent preprint, Lai worked out the quotient of generating functions of weighted lozenge tilings of two "half hexagons with lateral dents" which differ only in width. Lai achieved this by using "graphical condensation" (i.e., application of a certain Pfaffian identity to the weighted enumeration of matchings). The purpose of this note is to exhibit how this can be done by the Lindström--Gessel--Viennot method for nonintersecting lattice paths in a quite simple way. Basically the same observation, but restricted to mere enumeration (i.e., all weights of lozenge tilings are equal to $1$), is contained in a recent preprint of Condon.
