The minimal number of edges required to form a knot or link of type K is the edge number of K, and is denoted e(K). When knots are drawn with edges, they are appropriately called piecewise-linear or PL knots. This paper presents some edge number results for PL knots. Included are illustrations of and integer coordinates for the vertices of several prime PL knots.
@article{bwmeta1.element.bwnjournal-article-bcpv42i1p235bwm, author = {Meissen, Monica}, title = {Edge number results for piecewise-Linear knots}, journal = {Banach Center Publications}, volume = {43}, year = {1998}, pages = {235-242}, zbl = {0901.57015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p235bwm} }
Meissen, Monica. Edge number results for piecewise-Linear knots. Banach Center Publications, Tome 43 (1998) pp. 235-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p235bwm/
[000] [1] C. C. Adams, B. M. Brennan, D. L. Greilsheimer and A. K. Woo, Stick numbers and compositions of knots and links, Journal of Knot Theory and Its Ramifications, to appear. | Zbl 0884.57005
[001] [2] E. Flapan, Rigid and non-rigid achirality, Pacific Journal of Mathematics, 129(1):57-66, 1987. | Zbl 0594.57006
[002] [3] K. Hunt, KED, The University of Iowa. A computer program used to draw knots, http://www.cs.uiowa.edu/~hunt/knot.htm.
[003] [4] G. T. Jin, Polygon indices and superbridge indices, Journal of Knot Theory and Its Ramifications, to appear. | Zbl 0881.57002
[004] [5] G. T. Jin and H. S. Kim, Polygonal knots, Journal of the Korean Mathematical Society, 30(2):371-383, 1993.
[005] [6] K. C. Millett, Knotting of regular polygons in 3-space, in K. C. Millett and D. W. Sumners, editors, Random Knotting and Linking, pages 31-46. World Scientifis, Singapore, 1994. | Zbl 0838.57008
[006] [7] R. Randell, Invariants of piecewise-linear knots, this volume. | Zbl 0901.57014
[007] [8] D. Rolfsen, Knots and Links, Publish or Perish, Inc., Houston, 1990.
[008] [9] K. Smith, Generalized braid arrangements and related quotient spaces, PhD thesis, The University of Iowa, Iowa City, IA, USA, 1992.
[009] [10] Y-Q. Wu, MING, The University of Iowa, Iowa City, Iowa. A computer program used to draw knots, available via anonymous ftp at ftp.math.uiowa.edu/pub/wu/ming.