A new notion of parity is used to construct a simple strong invariant of free knots taking values in some group. The interval of the set of positive integers is considered containing all integers from 1 to a given number 2n and a chord diagram with a base point is defined as a partition of the set. For any positive integer, the equivalence of two chord diagram with base points implies the coincidence of the elements of the group corresponding to the words. The elements of the group are in one-to-one correspondence with the integer points in Euclidean space with last coordinate 0 or 1. Any chord diagram containing a completely adjoint chords has the property that the number of odd chords are even. The removal of odd chords preserves the triple of completely adjoint chords and if the triple again contains no odd chords, the chords are denoted by a group.

Authors

Journal

Number of issue

2

Language

English

Pages

697-700

Status

Published

Link

Volume

82

Year

2010

Organizations

^{1}Peoples Friendship University, ul. Miklukho-Maklaya 6, Moscow 117198, Russian Federation^{2}Moscow State Pedagogical University, ul. Malaya Pirogovskaya 1, Moscow 119882, Russian Federation

Keywords

Adjoints; Base points; Euclidean spaces; Integer point; Positive integers

Date of creation

19.10.2018

Date of change

19.10.2018

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