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

%I A172184 #14 Apr 30 2024 01:56:01
%S A172184 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,
%T A172184 0,0,2,3,2,0,1
%N A172184 Table read by antidiagonals: T(n,k) = number of prime knots up to nine crossings with determinant 2n+1 and signature 2k.
%D A172184 Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004. See p. 146. Fig. 6.6.
%e A172184 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.
%e A172184 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.
%e A172184 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.
%e A172184 Table begins:
%e A172184   =========================
%e A172184   Det s=0 s=2 s=4 s=6 s=8
%e A172184   =========================
%e A172184    1 | 1 | 0 | 0 | 0 | 0
%e A172184    3 | 0 | 1 | 0 | 1 | 0
%e A172184    5 | 1 | 0 | 1 | 0 | 0
%e A172184    7 | 0 | 2 | 0 | 1 | 0
%e A172184    9 | 3 | 0 | 0 | 0 | 1
%e A172184   11 | 0 | 2 | 0 | 0 | 0
%e A172184   13 | 2 | 0 | 2 | 0 | 0
%e A172184   15 | 0 | 3 | 0 | 0 | 0
%e A172184   17 | 2 | 0 | 2 | 0 | 0
%e A172184   =========================
%Y A172184 Cf. A002863, A172293, A172293, A172441, A172444, A172486.
%K A172184 nonn,tabl,more
%O A172184 1,11
%A A172184 _Jonathan Vos Post_, Nov 19 2010
%E A172184 Partially edited by _N. J. A. Sloane_, Jun 10 2019
%E A172184 Name edited by _Andrey Zabolotskiy_, Apr 29 2024