This paper aims to establish two bijections: from regions of the r-Shi arrangement to O-rooted labeled r-trees, and from regions of the r-Catalan arrangement to pairings of permutation and r-Dyck path. To this end, we introduce a cubic matrix for each region of the hyperplane arrangements. The first bijection is established by reading the positions of minimal positive entries in its column slices. The second one is obtained by reading the numbers of positive entries in its column slice, which turns out to be essentially the same as the bijection obtained by Duarte and Guedes de Oliveira [10] in 2019. Moreover, by reading the numbers of positive entries in its row slices we will recover the Pak-Stanley labeling, which is a celebrated bijection from regions of the r-Shi arrangement to r-parking functions.

本文旨在建立两个双射：从r- Shi排列的区域到O根标记的r-树，以及从r- Catalan排列的区域到置换和r的配对-戴克路径。为此，我们为超平面排列的每个区域引入一个立方矩阵。通过读取最小正条目在其列切片中的位置来建立第一个双射。第二个是通过读取其列切片中的正条目数获得的，这实际上与Duarte和Guedes de Oliveira [10]在2019年获得的双射相同。在其行切片中，我们将恢复Pak-Stanley标记，这是从r- Shi排列的区域到r-停车函数的著名双射。