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Abstract:We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a bijection proving this fact. Rushed paths turn out to be in bijection with one-sided trees, introduced by Durhuus and Unel, which have an asymptotic enumeration involving a stretched exponential. We conclude by presenting several other classes of related lattice paths and directed animals that may have similar asymptotic properties.
| Comments: | In Proceedings GASCom 2024, arXiv:2406.14588 |
| Subjects: | Combinatorics (math.CO); Discrete Mathematics (cs.DM) |
| Cite as: | arXiv:2403.08120 [math.CO] |
| (or arXiv:2403.08120v5 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2403.08120 arXiv-issued DOI via DataCite |
|
| Journal reference: | EPTCS 403, 2024, pp. 29-34 |
| Related DOI: | https://doi.org/10.4204/EPTCS.403.10
DOI(s) linking to related resources |
From: Axel Bacher [view email] [via EPTCS proxy]
[v1]
Tue, 12 Mar 2024 23:13:21 UTC (10 KB)
[v2]
Fri, 29 Mar 2024 22:50:08 UTC (16 KB)
[v3]
Mon, 24 Jun 2024 08:01:25 UTC (24 KB)
[v4]
Tue, 19 May 2026 15:21:13 UTC (18 KB)
[v5]
Thu, 21 May 2026 20:36:48 UTC (18 KB)
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