K12a1215
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+6 q^8-10 q^7+14 q^6-17 q^5+17 q^4-16 q^3+14 q^2-9 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-9 t^3+15 t^2-19 t+21-19 t^{-1} +15 t^{-2} -9 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-6 z^8-12 z^6-9 z^4-z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -8 z^8 a^{-4} +z^8 a^{-6} +6 z^6 a^{-2} -24 z^6 a^{-4} +6 z^6 a^{-6} +12 z^4 a^{-2} -33 z^4 a^{-4} +12 z^4 a^{-6} +10 z^2 a^{-2} -20 z^2 a^{-4} +9 z^2 a^{-6} +4 a^{-2} -5 a^{-4} +2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +9 z^{10} a^{-4} +5 z^{10} a^{-6} +3 z^9 a^{-1} -4 z^9 a^{-3} +7 z^9 a^{-7} -20 z^8 a^{-2} -42 z^8 a^{-4} -13 z^8 a^{-6} +8 z^8 a^{-8} +z^8-15 z^7 a^{-1} -9 z^7 a^{-3} -17 z^7 a^{-5} -16 z^7 a^{-7} +7 z^7 a^{-9} +34 z^6 a^{-2} +74 z^6 a^{-4} +13 z^6 a^{-6} -17 z^6 a^{-8} +5 z^6 a^{-10} -5 z^6+22 z^5 a^{-1} +22 z^5 a^{-3} +24 z^5 a^{-5} +10 z^5 a^{-7} -11 z^5 a^{-9} +3 z^5 a^{-11} -28 z^4 a^{-2} -70 z^4 a^{-4} -15 z^4 a^{-6} +14 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +7 z^4-9 z^3 a^{-1} -15 z^3 a^{-3} -16 z^3 a^{-5} +z^3 a^{-7} +8 z^3 a^{-9} -3 z^3 a^{-11} +14 z^2 a^{-2} +30 z^2 a^{-4} +10 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -z^2 a^{-12} -2 z^2+z a^{-1} +4 z a^{-3} +4 z a^{-5} -z a^{-7} -2 z a^{-9} -4 a^{-2} -5 a^{-4} -2 a^{-6} }[/math] |
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