论文标题
通过非晶格路径获得的某些六角形的某些区域生成的lozenge tiling的功能的商
The quotient of generating functions of lozenge tilings for certain regions derived from hexagons, obtained with non--intersecting lattice paths
论文作者
论文摘要
在最近的预印本中，莱（Lai）表明，产生两个“横向凹痕的半六角形的半六角形”的加权润滑块的功能，它们仅在宽度，因素方面差异很大，并且对于生成两个六季度六角形的加权lozenge tilsed lozenge tiles lozenge tiles Hexagons的函数也是如此。 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。 本注释的目的是展示如何通过lindström-gessel- viennot方法来实现晶格路径。对于“半六角形”的情况，基本上是相同的观察结果，但仅限于枚举（即，所有lozenge瓷砖的所有权重等于$ 1 $），在最近的condon预印本中包含。
In a recent preprint, Lai showed that the quotient of generating functions of weighted lozenge tilings of two "half hexagons with lateral dents", which differ only in width, factors nicely, and the same is true for the quotient of generating functions of weighted lozenge tilings of two "quarter hexagons with lateral dents". 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. For the case of "half hexagons", 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.
