论文标题
部分可观测时空混沌系统的无模型预测
Counting nearest faraway flats for Coxeter chambers
论文作者
论文摘要
在有限的Coxeter组$ W $中，并有两个给定的抛物线子组$ [x] $和$ [y] $的结合类别类别，我们计算了这些是全部支持的寄生抛物线子组，同时是简单的扩展名（即通过单个反射（即通过单个反射）（即单个反射）的一些标准副羊皮纸$ $ $ $ w $ [$ $ w]枚举由仅取决于两种抛物线类型的产品公式给出。我们的派生是无病例的，并将“全面支持”属性的几何解释与涉及Crapo Beta不变的双重计数论点结合在一起。作为推论，这种方法提供了第一个无案证明肖普顿公式的证明，以实现真正的反思组$ w $中全面支持的数量。
In a finite Coxeter group $W$ and with two given conjugacy classes of parabolic subgroups $[X]$ and $[Y]$, we count those parabolic subgroups of $W$ in $[Y]$ that are full support, while simultaneously being simple extensions (i.e., extensions by a single reflection) of some standard parabolic subgroup of $W$ in $[X]$. The enumeration is given by a product formula that depends only on the two parabolic types. Our derivation is case-free and combines a geometric interpretation of the "full support" property with a double counting argument involving Crapo's beta invariant. As a corollary, this approach gives the first case-free proof of Chapoton's formula for the number of reflections of full support in a real reflection group $W$.
