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- W4285704037 abstract "Various lattice path models are reviewed. The enumeration is done using generating functions. A few bijective considerations are woven in as well. The kernel method is often used. Computer algebra was an essential tool. Some results are new, some have appeared before. The lattice path models we treated, are: Hoppy's walks, the combinatorics of sequence A002212 in cite{OEIS} (skew Dyck paths, Schroder paths, Hex-trees, decorated ordered trees, multi-edge trees, etc.) Weighted unary-binary trees also occur, and we could improve on our old paper on Horton-Strahler numbers cite{FlPr86}, by using a different substitution. Some material on ternary trees appears as well, as on Motzkin numbers and paths (a model due to Retakh), and a new concept called amplitude that was found in cite{irene}. Some new results on Deutsch paths in a strip are included as well. During the Covid period, I spent much time with this beautiful concept that I dare to call Deutsch paths, since Emeric Deutsch stands at the beginning with a problem that he posted in the American Mathematical Monthly some 20 years ago. Peaks and valleys, studied by Rainer Kemp 40 years under the names textsc{max}-turns and textsc{min}-turns, are revisited with a more modern approach, streamlining the analysis, relying on the `subcritical case' (named so by Philippe Flajolet), the adding a new slice technique and once again the kernel method." @default.
- W4285704037 created "2022-07-18" @default.
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- W4285704037 date "2021-11-29" @default.
- W4285704037 modified "2023-09-27" @default.
- W4285704037 title "A walk in my lattice path garden" @default.
- W4285704037 doi "https://doi.org/10.48550/arxiv.2111.14797" @default.
- W4285704037 hasPublicationYear "2021" @default.
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