A172184 Table read by antidiagonals: T(n,k) = number of prime knots up to nine crossings with determinant 2n+1 and signature 2k.

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

Author

Jonathan Vos Post, Nov 19 2010

Keywords

• nonn
• tabl
• more

Examples

			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
  =========================
		

References

• Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004. See p. 146. Fig. 6.6.

Crossrefs

Cf. A002863, A172293, A172293, A172441, A172444, A172486.

Extensions

Partially edited by N. J. A. Sloane, Jun 10 2019

Name edited by Andrey Zabolotskiy, Apr 29 2024