论文标题
$ n $ -cylinder方形的表面贡献$ \ Mathcal {H}（2G-2）$
Contribution of $n$-cylinder square-tiled surfaces to Masur-Veech volume of $\mathcal{H}(2g-2)$
论文作者
论文摘要
我们找到了$ n $ -Cylinder Square Arfaces of $ \ Mathcal {H}（H}（2G-2）$的贡献的生成功能。这是Sauvaget通过相交理论获得的总体积的生成函数的双变量概括。但是，我们的方法纯粹是组合。它依赖于某些公制色带图的计数函数的研究。它们的高度术语是多项式，其（标准化的）系数是某些公制平面树的基础。这些多项式是Kontsevich多项式的类似物，它们是他的Witten猜想证明的一部分。
We find the generating function for the contributions of $n$-cylinder square-tiled surfaces to the Masur-Veech volume of $\mathcal{H}(2g-2)$. It is a bivariate generalization of the generating function for the total volumes obtained by Sauvaget via intersection theory. Our approach is, however, purely combinatorial. It relies on the study of counting functions for certain families of metric ribbon graphs. Their top-degree terms are polynomials, whose (normalized) coefficients are cardinalities of certain families of metric plane trees. These polynomials are analogues of Kontsevich polynomials that appear as part of his proof of Witten's conjecture.
