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

PERIODIC VIRTUAL LINKS AND THE BINARY BRACKET POLYNOMIAL.

JEONG, MYEONG-JU; PARK, CHAN-YOUNG