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The incompatibility of crossing number and bridge number for knot diagrams Appendix. A note on Wirtinger number and flypes by Ryan Blair and Nathaniel Morrison

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The incompatibility of crossing number and bridge number for knot diagrams Appendix. A note on Wirtinger number and flypes by Ryan Blair and Nathaniel Morrison. / Blair, Ryan; Ozawa, Makoto; Kjuchukova, Alexandra et al.
2 p. 7 ed. Elsevier. 2019, Appendix to a journal article . (Discrete Mathematics).

Research output: Other contribution

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Blair, Ryan ; Ozawa, Makoto ; Kjuchukova, Alexandra et al. / The incompatibility of crossing number and bridge number for knot diagrams Appendix. A note on Wirtinger number and flypes by Ryan Blair and Nathaniel Morrison. 2019. Elsevier. 2 p. (Discrete Mathematics).

Bibtex

@misc{a79bc166bdfe4b7e9bb4cf779ccd2493,
title = "The incompatibility of crossing number and bridge number for knot diagrams Appendix. A note on Wirtinger number and flypes by Ryan Blair and Nathaniel Morrison",
abstract = "We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.",
author = "Ryan Blair and Makoto Ozawa and Alexandra Kjuchukova and Nathaniel Morrison",
note = "I helped author the appendix to this article, “A note on Wirtinger number and flypes,” rather than the main article. My name therefore appears above the appendix instead of in the main author line.",
year = "2019",
month = jul,
day = "1",
doi = "10.1016/j.disc.2019.03.013",
language = "English",
volume = "342",
series = "Discrete Mathematics",
publisher = "Elsevier",
edition = "7",
type = "Other",

}

RIS

TY - GEN

T1 - The incompatibility of crossing number and bridge number for knot diagrams Appendix. A note on Wirtinger number and flypes by Ryan Blair and Nathaniel Morrison

AU - Blair, Ryan

AU - Ozawa, Makoto

AU - Kjuchukova, Alexandra

AU - Morrison, Nathaniel

N1 - I helped author the appendix to this article, “A note on Wirtinger number and flypes,” rather than the main article. My name therefore appears above the appendix instead of in the main author line.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.

AB - We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.

U2 - 10.1016/j.disc.2019.03.013

DO - 10.1016/j.disc.2019.03.013

M3 - Other contribution

VL - 342

T3 - Discrete Mathematics

PB - Elsevier

ER -