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Combinatorics of Seaweed Meanders

  • Maximus Lu
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Abstract

We show that the index of a uniformly random seaweed meander satisfies a central limit theorem and is asymptotically equidistributed with respect to any modulus. We also extend work by Archer, Geary, and Laudone on the enumeration of seaweed meanders whose compositions have restricted parts. Finally, we give a connection to billiards in triangular shapes, which is related to a result of Eu, Fu, and Hsu.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026combinatorics,
  title = {{Combinatorics of Seaweed Meanders}},
  author = {Maximus Lu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25547},
  eprint = {2610.25547},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25547},
}
RIS
TY  - UNPB
TI  - Combinatorics of Seaweed Meanders
AU  - Maximus Lu
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25547
UR  - https://arxiv.org/abs/2610.25547
AB  - We show that the index of a uniformly random seaweed meander satisfies a central limit theorem and is asymptotically equidistributed with respect to any modulus. We also extend work by Archer, Geary, and Laudone on the enumeration of seaweed meanders whose compositions have restricted parts. Finally, we give a connection to billiards in triangular shapes, which is related to a result of Eu, Fu, and Hsu.
ER  -