论文标题
Q，T-Catalan措施
q,t-Catalan measures
论文作者
论文摘要
我们介绍了$ Q，T $ -CATALAN措施，这是一系列在$ \ Mathbb {r}^2 $上进行的多项式措施。这些措施是根据适当的面积，DINV和弹跳统计数据定义的，对飞机中的路径连续家庭有很多，并且与$ Q，t $ -catalan数字具有许多组合相似之处。我们的主要结果意识到$ Q，T $ -CATALAN量度为较高$ Q，t $ -catalan编号$ c^{（m）} _ n（q，t）$作为$ m \ to \ infty $。我们还对$ Q，T $ -CATALAN措施进行了几何解释。它们是$ \ Mathbb {c}^2 $ opartual Hilbert Shemes参数化的duistermaat-Heckman量度。
We introduce the $q,t$-Catalan measures, a sequence of piece-wise polynomial measures on $\mathbb{R}^2$. These measures are defined in terms of suitable area, dinv, and bounce statistics on continuous families of paths in the plane, and have many combinatorial similarities to the $q,t$-Catalan numbers. Our main result realizes the $q,t$-Catalan measures as a limit of higher $q,t$-Catalan numbers $C^{(m)}_n(q,t)$ as $m\to\infty$. We also give a geometric interpretation of the $q,t$-Catalan measures. They are the Duistermaat-Heckman measures of the punctual Hilbert schemes parametrizing subschemes of $\mathbb{C}^2$ supported at the origin.
