Boundary Algorithms for Thompson Groups

Abstract

We construct a deterministic Farey-boundary algorithm converting a cyclic prefix table for an element of T into a word in addressed boundary flips. The reduction uses rational boundary pairs and cyclic order, with a marked edge determining the residual modular correction. Its unmarked stage uses at most twice the minimum number of diagonal exchanges. For input size s, the complete output has O(s) factors, encoded length O(s²), and running time O(s³). Adjoining shuffles extends the construction to V with polynomial bounds. We also give explicit boundary generating sets and their local flip--shuffle relations. Changes of generators in the Lochak--Schneps and Bleak--Quick presentations yield a two-flip presentation of T and a presentation of V with two flips, one shuffle, and nine relations.

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BibTeX RIS

BibTeX

@misc{zeytin2026boundary,
  title = {{Boundary Algorithms for Thompson Groups}},
  author = {Ayberk Zeytin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07293},
  eprint = {2610.07293},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07293},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Boundary Algorithms for Thompson Groups
AU  - Ayberk Zeytin
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07293
UR  - https://arxiv.org/abs/2610.07293
AB  - We construct a deterministic Farey-boundary algorithm converting a cyclic prefix table for an element of T into a word in addressed boundary flips. The reduction uses rational boundary pairs and cyclic order, with a marked edge determining the residual modular correction. Its unmarked stage uses at most twice the minimum number of diagonal exchanges. For input size s, the complete output has O(s) factors, encoded length O(s^2), and running time O(s^3). Adjoining shuffles extends the construction to V with polynomial bounds. We also give explicit boundary generating sets and their local flip--shuffle relations. Changes of generators in the Lochak--Schneps and Bleak--Quick presentations yield a two-flip presentation of T and a presentation of V with two flips, one shuffle, and nine relations.
ER  -

Abstract

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