Delta-crossing number for knots

Autor:	Yoko Sakamoto, Yasutaka Nakanishi, Shin Satoh
Rok vydání:	2015
Předmět:	Combinatorics Delta Knot (unit) Crossing number (knot theory) Skein relation Diagram Geometry and Topology Mathematics::Geometric Topology Upper and lower bounds Tangle Mathematics Knot theory
Zdroj:	Topology and its Applications. 196:771-776
ISSN:	0166-8641
Popis:	A Delta-crossing tangle is a tangle of three arcs with three crossings, which appears in a Delta move (or Delta unknotting operation). A Delta-crossing diagram is a diagram which can be decomposed into Delta-crossing tangles joined by simple arcs. We prove that every knot has a Delta-crossing diagram, and then investigate the Delta-crossing number which is the minimum number of Delta-crossing tangles among all Delta-crossing diagrams of the given knot. We obtain upper and lower bounds on the number in terms of the ordinal crossing number and genus. We also determine the number for prime knots with nine crossings or less except six knots.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d66f5889427188035c6a481a40223d04 https://doi.org/10.1016/j.topol.2015.05.044 Zobrazit plný text záznamu Full Text from ScienceDirect