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XXIII.—Amphicheiral Knots

Published online by Cambridge University Press:  06 July 2012

Mary Gertrude Haseman
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Extract

The intrinsic symbol of an amphicheiral knot is based on the idea of the sequence of the crossings; it replaces each letter of the alphabetical symbol by a number equal to one-half of the number of crossings intervening before the next occurrence of that letter as the knot is traversed in a definite direction. Hence it is seen that two knots, which have the same intrinsic symbol, are identical. Since the same number of pairs of crossings must elapse before the next occurrence of corresponding crossings of two identical knots when the knots are traversed in a given direction, it is seen that the converse is true also. It may be necessary to consider the complementary intrinsic symbol in order to detect identical knots.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 52 , Issue 3 , September 1920 , pp. 597 - 602
Copyright
Copyright © Royal Society of Edinburgh 1920

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References

page 597 note * Haseman, M. G., Trans. Roy. Soc. Edin., vol. lii, p. 235.Google Scholar

page 598 note * Tait, , Trans. Roy. Soc. Edin., vol. xxxii, p. 497.Google Scholar

page 598 note † Ibid., Plate LXXIX.

page 598 note ‡ Ibid., p. 497.

page 600 note * The numbers at the lower right-hand corners are Tait's numbers.

page 601 note * Haseman, M. G., Trans. Roy. Soc. Edin., vol. lii, p. 254.Google Scholar