Open AccessCoding Knots by T-Graphs
Author(s) -
O. N. Biryukov,
О Н Бирюков
Publication year - 2020
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2020-66-4-531-543
Subject(s) - torsion (gastropod) , knot (papermaking) , coding (social sciences) , computer science , knot theory , mathematics , combinatorics , theoretical computer science , engineering , anatomy , biology , statistics , chemical engineering
In this paper, knots are considered as smooth embeddings of a circle into 3 defined by their flat diagrams. We propose a new method of coding knots by T-graphs describing the torsion structure on a flat diagram. For this method of coding, we introduce conceptions of a cycle and a block and describe transformations of T-graphs under the first and the third Reidemeister moves applied to the flat diagram of a knot.