An index polynomial invariant for flat virtual knots

We introduce a polynomial invariant of flat virtual knots which is sometimes useful for determining whether given flat virtual knots are invertible or not, and for finding the virtual crossing number of flat virtual knots. Also we give several properties of the polynomial invariant for flat virtual...

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Published inEuropean journal of combinatorics Vol. 31; no. 8; pp. 2130 - 2140
Main Authors Im, Young Ho, Lee, Kyeonghui, Son, Heeok
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2010
Subjects
Combinatorial analysis
Invariants
Knots
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Summary:We introduce a polynomial invariant of flat virtual knots which is sometimes useful for determining whether given flat virtual knots are invertible or not, and for finding the virtual crossing number of flat virtual knots. Also we give several properties of the polynomial invariant for flat virtual knots and examples. In particular, we show that the conjecture given by Hrencecin and Kauffman (2003) [8] is true and so an infinite class of flat virtual knots { U n } ( n = 1 , 2 , … ) are mutually distinct.
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ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2010.06.003