Abstract
The geometry of polygonal knots in the cubic lattice may be used to define some knot invariants. One such invariant is the minimal edge number, which is the minimum number of edges necessary (and sufficient) to construct a lattice knot of given type. In addition, one may also define the minimal (unfolded) surface number, and the minimal (unfolded) boundary number; these are the minimum number of 2-cells necessary to construct an unfolded lattice Seifert surface of a given knot type in the lattice, and the minimum number of edges necessary in a lattice knot to gaurantee the existence of an unfolded lattice Seifert surface. In addition, I derive some relations amongst these invariants.
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© 1996 Springer-Verlag New York, Inc.
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Van Rensburg, E.J.J. (1996). Lattice Invariants for Knots. In: Mesirov, J.P., Schulten, K., Sumners, D.W. (eds) Mathematical Approaches to Biomolecular Structure and Dynamics. The IMA Volumes in Mathematics and its Applications, vol 82. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4066-2_2
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DOI: https://doi.org/10.1007/978-1-4612-4066-2_2
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