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A172184
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Table read by antidiagonals: T(n,k) = number of prime knots with determinant 2n+1 and signature 2k.
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7
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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
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OFFSET
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1,11
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REFERENCES
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Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004. See p. 146. Fig. 6.6.
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LINKS
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EXAMPLE
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T(0,0) = 1 because the only prime knot with determinant 2*0+1=1 and s=0 is 0_1, the unknot.
T(1,1) = 1 because the only prime knot 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 determinant 2*1+1=3 and s=6 is 8_19.
Table begins:
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Det…s=0…s=2…s=4…s=6…s=8
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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