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• W3024164089 abstract "Associated with the $r$-Shi arrangement and $r$-Catalan arrangement in $Bbb{R}^n$, we introduce a cubic matrix for each region to establish two bijections in a uniform way. Firstly, the positions of minimal positive entries in 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 of positive entries in column slices of the cubic matrix will give a bijection from regions of the $r$-Catalan arrangement to pairings of permutation and $r$-Dyck path. Moreover, the numbers of positive entries in row slices of the cubic matrix will recover the Pak-Stanley labeling, a celebrated bijection from regions of the $r$-Shi arrangement to $r$-parking functions." @default.
• W3024164089 created "2020-05-21" @default.
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• W3024164089 date "2020-05-18" @default.
• W3024164089 modified "2023-10-16" @default.
• W3024164089 title "Bijections on $r$-Shi and $r$-Catalan Arrangements" @default.
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• W3024164089 doi "https://doi.org/10.48550/arxiv.2005.08574" @default.
• W3024164089 hasPublicationYear "2020" @default.
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