论文标题
加泰罗尼亚人的数字，停车职能，定居者和非交通性希尔伯特计划
Catalan numbers, parking functions, permutahedra and noncommutative Hilbert schemes
论文作者
论文摘要
我们在$ \ Mathbb {r}^n $中的某个Zonotope中的积分点之间的积分点之间的显式$ s_n $ - equivariant射击，与Perminator上的组合等同，与$ m $ n $ $ n $的$ m $ m $式标记函数。这种培训限制在常规$ s_n $ -orbits和$（m，n）$ - dyck路径之间的两次培训，该路径的数量由大惊小怪的 - catalan number $ a_ {n}（m，1）$给出。我们的动机来自研究非交通性希尔伯特计划的倾斜捆绑包。作为一方面的结果，我们使用这些倾斜束来构建非交通性希尔伯特方案的派生类别的半正交分解。
We find an explicit $S_n$-equivariant bijection between the integral points in a certain zonotope in $\mathbb{R}^n$, combinatorially equivalent to the permutahedron, and the set of $m$-parking functions of length $n$. This bijection restricts to a bijection between the regular $S_n$-orbits and $(m,n)$-Dyck paths, the number of which is given by the Fuss-Catalan number $A_{n}(m,1)$. Our motivation came from studying tilting bundles on noncommutative Hilbert schemes. As a side result we use these tilting bundles to construct a semi-orthogonal decomposition of the derived category of noncommutative Hilbert schemes.
