login
A172184
Table read by antidiagonals: T(n,k) = number of prime knots up to nine crossings with determinant 2n+1 and signature 2k.
7
1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 1
OFFSET
1,11
REFERENCES
Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004. See p. 146. Fig. 6.6.
EXAMPLE
T(0,0) = 1 because the only prime knot with no more than 9 crossings with determinant 2*0+1=1 and s=0 is 0_1, the unknot.
T(1,1) = 1 because the only prime knot with no more than 9 crossings with determinant 2*1+1=3 and s=2 is 3_1, the left-handed trefoil.
T(1,3) = 1 because the only prime knot with no more than 9 crossings with determinant 2*1+1=3 and s=6 is 8_19.
Table begins:
=========================
Det s=0 s=2 s=4 s=6 s=8
=========================
1 | 1 | 0 | 0 | 0 | 0
3 | 0 | 1 | 0 | 1 | 0
5 | 1 | 0 | 1 | 0 | 0
7 | 0 | 2 | 0 | 1 | 0
9 | 3 | 0 | 0 | 0 | 1
11 | 0 | 2 | 0 | 0 | 0
13 | 2 | 0 | 2 | 0 | 0
15 | 0 | 3 | 0 | 0 | 0
17 | 2 | 0 | 2 | 0 | 0
=========================
CROSSREFS
KEYWORD
nonn,tabl,more
AUTHOR
Jonathan Vos Post, Nov 19 2010
EXTENSIONS
Partially edited by N. J. A. Sloane, Jun 10 2019
Name edited by Andrey Zabolotskiy, Apr 29 2024
STATUS
approved