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- W4320166892 abstract "Motzkin paths with air pockets (MAP) of the first kind are defined as a generalization of Dyck paths with air pockets. They are lattice paths in $mathbb{N}^2$ starting at the origin made of steps $U=(1,1)$, $D_k=(1,-k)$, $kgeq 1$ and $H=(1,0)$, where two down-steps cannot be consecutive. We enumerate MAP and their prefixes avoiding peaks (resp. valleys, resp. double rise) according to the length, the type of the last step, and the height of its end-point. We express our results using Riordan arrays. Finally, we provide constructive bijections between these paths and restricted Dyck and Motzkin paths." @default.
- W4320166892 created "2023-02-13" @default.
- W4320166892 creator A5022445136 @default.
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- W4320166892 date "2023-01-25" @default.
- W4320166892 modified "2023-09-26" @default.
- W4320166892 title "Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises" @default.
- W4320166892 doi "https://doi.org/10.48550/arxiv.2301.10449" @default.
- W4320166892 hasPublicationYear "2023" @default.
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