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PreprintarXiv licencearXiv

Delta-Unknotting Number for Montesinos Knots

  • Kazumichi Nakamura
Open at sourcePDFDOICite

Abstract

The Δ-unknotting number for a knot is defined as the minimum number of Δ-moves needed to deform the knot into the trivial knot. In this paper, we determine the Δ-unknotting numbers for certain families of Montesinos knots. Using results on pretzel knots and two-bridge knots, we prove that for these families the Δ-unknotting number equals the absolute value of the second coefficient of the Conway polynomial. In particular, every positive pretzel knot belongs to these families, and certain two-bridge knots also belong to them.

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Cite

BibTeXRIS
BibTeX
@misc{nakamura2026deltaunknotting,
  title = {{Delta-Unknotting Number for Montesinos Knots}},
  author = {Kazumichi Nakamura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14522},
  eprint = {2609.14522},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14522},
}
RIS
TY  - UNPB
TI  - Delta-Unknotting Number for Montesinos Knots
AU  - Kazumichi Nakamura
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14522
UR  - https://arxiv.org/abs/2609.14522
AB  - The Δ-unknotting number for a knot is defined as the minimum number of Δ-moves needed to deform the knot into the trivial knot. In this paper, we determine the Δ-unknotting numbers for certain families of Montesinos knots. Using results on pretzel knots and two-bridge knots, we prove that for these families the Δ-unknotting number equals the absolute value of the second coefficient of the Conway polynomial. In particular, every positive pretzel knot belongs to these families, and certain two-bridge knots also belong to them.
ER  -