We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
THE POLE DIAGRAM AND THE MIYAZAWA POLYNOMIAL.
- Authors
Ishii, Atsushi
- Abstract
We introduce the pole diagram, which helps to retrieve information from a knot diagram when we smooth crossings. By using the notion, we define a bracket polynomial for the Miyazawa polynomial. The bracket polynomial gives a simple definition and evaluation for the Miyazawa polynomial. Then we show that the virtual crossing number of a virtualized alternating link is determined by its diagram. Furthermore, we construct infinitely many virtual link diagrams which attain the minimal real and virtual crossing numbers together.
- Subjects
GRAPHIC methods; POLYNOMIALS; GEOMETRICAL drawing; ALGEBRA; APPROXIMATION theory
- Publication
International Journal of Mathematics, 2008, Vol 19, Issue 2, p193
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X08004601