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Associated with the $r$-Shi arrangement and $r$-Catalan arrangement in$\Bbb{R}^n$, we introduce a cubic matrix for each region to establish twobijections in a uniform way. Firstly, the positions of minimal positive entriesin column slices of the cubic matrix will give a bijection from regions of the$r$-Shi arrangement to $O$-rooted labeled $r$-trees. Secondly, the numbers ofpositive entries in column slices of the cubic matrix will give a bijectionfrom regions of the $r$-Catalan arrangement to pairings of permutation and$r$-Dyck path. Moreover, the numbers of positive entries in row slices of thecubic matrix will recover the Pak-Stanley labeling, a celebrated bijection fromregions of the $r$-Shi arrangement to $r$-parking functions.

Bijections on $r$-Shi and $r$-Catalan Arrangements