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Title

PERIODIC VIRTUAL LINKS AND THE BINARY BRACKET POLYNOMIAL.

Authors

JEONG, MYEONG-JU; PARK, CHAN-YOUNG

Abstract

L. H. Kauffman defined the binary bracket polynomial of a virtual link by introducing binary labelings into the states of a virtual link diagram. We use the invariant by a slight modification, and call it the modified b-polynomial. We prove that if a virtual link K has a period pl for a prime p and a positive integer l, then the modified b-polynomial InvK (A) of K is congruent to InvK* (A) modulo p and A4pl-1 where K* is the mirror image of K. We exhibit examples of virtual links whose periods are completely determined by the invariant.

Subjects

POLYNOMIALS; GRAPH labelings; NATURAL numbers; PRIME numbers; MIRROR images; INVARIANT manifolds

Publication

Journal of Knot Theory & Its Ramifications, 2012, Vol 21, Issue 3, p1250002-1

ISSN

0218-2165

Publication type

Academic Journal

DOI

10.1142/S0218216511009789

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