Search: id:A122059
Results 1-1 of 1 results found.

%I A122059
%S A122059 1,0,0,1,1,2,3,0,4
%N A122059 Number of different polygonal knots with n straight line segments.
%C A122059 A spatial polygon is a finite set of straght line segments in R3 which 
               intersect only at their endpoints; the lines are called edges and 
               their endpoints are called vertices; exactly two edges meet at every 
               vertex. There must be at least 3 edges to make a triangle (the trivial 
               knot) and it is not hard to show that a knotted polygon must have 
               at least 6 edges. "Enumerating these polygons soon becomes impracticable 
               because the number of cases explodes as n increases."
%D A122059 Peter Cromwell, Knots and Links, Cambridge University Press, 2004, Sec. 
               1.3 (pp. 5-8), Appendix E.
%H A122059 Robert G. Scharein, <a href="http://www.colab.sfu.ca/KnotPlot/sticknumbers/
               ">Stick numbers for minimal stick knots</a>, Feb 15, 2004.
%H A122059 Bryson R. Payne, <a href="http://www.oglethorpe.edu/faculty/~j_nardo/
               knots/advanced.htm">Advanced Knot Theory Topics</a>, Knot Theory 
               Online.
%e A122059 a(3) = 1 because the unique polygonal knot of 3 edges can be drawn with 
               vertex coordinates (4,9,5), (7,-9,5), (-9,-3,5).
%e A122059 a(6) = 1 because the unique polygonal knot of 6 edges can be drawn with 
               vertex coordinates (4,9,5), (-7,-7,-5), (7,-9,5), (-1,9,-5), (-9,
               -3,5), (9,-5,-5).
%e A122059 a(7) = 1 because the unique polygonal knot of 7 edges can be drawn with 
               vertex coordinates (9,-6,3), (-4,-7,3), (1,7,2), (-9,2,-10), (4,-5,
               10), (2,2,-2), (-5,2,5).
%Y A122059 Cf. A002863 Number of prime knots with n crossings.
%Y A122059 Sequence in context: A035549 A137663 A161628 this_sequence A164917 A166238 
               A014197
%Y A122059 Adjacent sequences: A122056 A122057 A122058 this_sequence A122060 A122061 
               A122062
%K A122059 hard,nonn
%O A122059 3,6
%A A122059 Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 14 2006

Search completed in 0.001 seconds