Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species
Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species
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发表时间：
2019-04
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通讯作者：
Norihiro Nakashima;S. Tsujie
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作者：
Norihiro Nakashima;S. Tsujie
超平面排列的平面数是Bell数和第二类斯特林数的推广。1998年，罗伯特·吉尔（Robert Gill）利用物种给出了扩展的卡塔兰安排的平坦数的指数生成函数。本文引入了推广的Catalan和Shi排列的平坦类，它们是通过集合和列表的迭代替换而给出的。此外，我们列举了单位的这些安排的无限矩阵。
The number of flats of a hyperplane arrangement is considered as a generalization of the Bell number and the Stirling number of the second kind. In 1998, Robert Gill gave the exponential generating function of the number of flats of the extended Catalan arrangements, using species. In this article, we introduce the species of flats of the extended Catalan and Shi arrangements and they are given by iterated substitution of species of sets and lists. Moreover, we enumerate the flats of these arrangements in terms of infinite matrices.