K12n832
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2-5 q^{-1} +9 q^{-2} -13 q^{-3} +17 q^{-4} -17 q^{-5} +16 q^{-6} -13 q^{-7} +8 q^{-8} -4 q^{-9} + q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+13 t^2-23 t+27-23 t^{-1} +13 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-5 z^4+2 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^8+z^2 a^8-a^8-z^6 a^6-z^4 a^6+3 z^2 a^6+2 a^6-2 z^6 a^4-7 z^4 a^4-7 z^2 a^4-2 a^4+2 z^4 a^2+5 z^2 a^2+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^4 a^{12}+4 z^5 a^{11}-2 z^3 a^{11}+8 z^6 a^{10}-7 z^4 a^{10}+z^2 a^{10}+11 z^7 a^9-15 z^5 a^9+6 z^3 a^9+10 z^8 a^8-15 z^6 a^8+7 z^4 a^8-z^2 a^8-a^8+5 z^9 a^7+2 z^7 a^7-22 z^5 a^7+18 z^3 a^7-4 z a^7+z^{10} a^6+12 z^8 a^6-34 z^6 a^6+23 z^4 a^6-2 z^2 a^6-2 a^6+6 z^9 a^5-8 z^7 a^5-13 z^5 a^5+20 z^3 a^5-6 z a^5+z^{10} a^4+2 z^8 a^4-8 z^6 a^4-z^4 a^4+7 z^2 a^4-2 a^4+z^9 a^3+z^7 a^3-10 z^5 a^3+10 z^3 a^3-2 z a^3+3 z^6 a^2-9 z^4 a^2+7 z^2 a^2-2 a^2 }[/math] |
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