Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0834.57004
Diao, Yuanan
The number of smallest knots on the cubic lattice. (English)
[J] J. Stat. Phys. 74, No.5-6, 1247-1254 (1994). ISSN 0022-4715; ISSN 1572-9613/e

Polygons on the cubic lattice are piecewise linear simple closed curves such that each linear piece is of unit length and its vertices are on the cubic lattice. Such polygons are used to simulate the behavior of (thick) random closed curves found in models from chemistry and physics. Knotting of such polygons is an interesting problem. It has been shown that a polygon on the cubic lattice needs at least 24 edges to form a knot. It is shown that the only knots one can obtain with 24 edges are the trefoils. Furthermore, by classifying the projections of the polygons on a plane, we are able to enumerate all possible knotted polygons on the cubic lattice with 24 edges. The number of such unrooted knots on the cubic lattice is 3496.
[Y.Diao (Marietta)]

MSC 2000:: *57M25 Knots and links in the 3-sphere
82B99 Equilibrium statistical mechanics
60B99 Probability theory on general structures

Keywords: self-avoiding walks; polygons on the cubic lattice; knot; knotted polygons on the cubic lattice with 24 edges

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]