Catalan numbers and noncommutative Hilbert schemes

IF 0.5 4区 数学 Q3 MATHEMATICS
Valery Lunts, Špela Špenko, Michel Van Den Bergh
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引用次数: 0

Abstract

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.
加泰罗尼亚数和非交换希尔伯特方案
我们发现在$\mathbb{R}^n$中的某一宗斜面上的积分点与长度为n的m-停泊函数集之间有一个明确的$S_n$-等价偏射,其组合等价于过正多面体。这个偏射限制了正则$S_n$-轨道与$(m, n)$-戴克路径之间的偏射,其数量由福斯-卡塔兰数$A_n (m, 1)$给出。我们的研究动机来自于对非交换希尔伯特方案上倾斜束的研究。作为附带结果,我们利用这些倾斜束构建了非交换希尔伯特方案派生类的半正交分解。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.
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