Edge number results for piecewise-Linear knots

Monica Meissen

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 235-242
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Meissen, Monica. "Edge number results for piecewise-Linear knots." Banach Center Publications 42.1 (1998): 235-242. <http://eudml.org/doc/208808>.

@article{Meissen1998,
abstract = {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.},
author = {Meissen, Monica},
journal = {Banach Center Publications},
keywords = {PL knot; edge number},
language = {eng},
number = {1},
pages = {235-242},
title = {Edge number results for piecewise-Linear knots},
url = {http://eudml.org/doc/208808},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Meissen, Monica
TI - Edge number results for piecewise-Linear knots
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 235
EP - 242
AB - 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.
LA - eng
KW - PL knot; edge number
UR - http://eudml.org/doc/208808
ER -

References

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  1. [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. Zbl0884.57005
  2. [2] E. Flapan, Rigid and non-rigid achirality, Pacific Journal of Mathematics, 129(1):57-66, 1987. Zbl0594.57006
  3. [3] K. Hunt, KED, The University of Iowa. A computer program used to draw knots, http://www.cs.uiowa.edu/~hunt/knot.htm. 
  4. [4] G. T. Jin, Polygon indices and superbridge indices, Journal of Knot Theory and Its Ramifications, to appear. Zbl0881.57002
  5. [5] G. T. Jin and H. S. Kim, Polygonal knots, Journal of the Korean Mathematical Society, 30(2):371-383, 1993. 
  6. [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. Zbl0838.57008
  7. [7] R. Randell, Invariants of piecewise-linear knots, this volume. Zbl0901.57014
  8. [8] D. Rolfsen, Knots and Links, Publish or Perish, Inc., Houston, 1990. 
  9. [9] K. Smith, Generalized braid arrangements and related quotient spaces, PhD thesis, The University of Iowa, Iowa City, IA, USA, 1992. 
  10. [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. 

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