1998
DOI: 10.1142/9789812796073_0007
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Minimal Edge Piecewise Linear Knots

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Cited by 23 publications
(38 citation statements)
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“…These two questions give a sense of the degree of difficulty in describing the knot theory of equilateral polygons in 3-space beyond those having 8 or fewer edges. For these fundamental cases, one knows more about the nature and structure on knotting [CM98,Cal98,Cal01a,Cal01b].…”
Section: Knots Ephemeral Knots and Slipknotsmentioning
confidence: 99%
“…These two questions give a sense of the degree of difficulty in describing the knot theory of equilateral polygons in 3-space beyond those having 8 or fewer edges. For these fundamental cases, one knows more about the nature and structure on knotting [CM98,Cal98,Cal01a,Cal01b].…”
Section: Knots Ephemeral Knots and Slipknotsmentioning
confidence: 99%
“…The p [K] in the fourth column of Table W is the polygon index of K which is the minimal number of straight edges needed to form a polygonal knot equivalent to K. The values and the estimates of polygon index in the table were collected from various articles [2,3,6,10]. Roughly speaking, any local extrema can occur only at vertices and hence no more than one half of the vertices can attain local maxima.…”
Section: Primes Knots Up To Nine Crossingsmentioning
confidence: 99%
“…The number or the upper limit of the range of numbers in the second column of the table is the largest integer not exceeding one half of the minimal edge number or the best-known minimal edge number [2,3,7,11]. For the five knots, 3 1 , 4 1 , 5 1 , 5 2 and 8 19 , this number is equal to the harmonic degree [18].…”
Section: Prime Knots Up To 9 Crossingsmentioning
confidence: 99%