K12a923
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+7 q^{11}-12 q^{10}+16 q^9-20 q^8+20 q^7-19 q^6+16 q^5-10 q^4+7 q^3-3 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-18 t^2+25 t-27+25 t^{-1} -18 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-4 z^4+2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -4 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +4 z^4 a^{-4} -2 z^4 a^{-6} -10 z^4 a^{-8} +4 z^4 a^{-10} +4 z^2 a^{-4} +6 z^2 a^{-6} -13 z^2 a^{-8} +5 z^2 a^{-10} + a^{-4} +5 a^{-6} -8 a^{-8} +3 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +4 z^{10} a^{-6} +10 z^{10} a^{-8} +6 z^{10} a^{-10} +3 z^9 a^{-5} -z^9 a^{-7} +5 z^9 a^{-9} +9 z^9 a^{-11} +z^8 a^{-4} -17 z^8 a^{-6} -40 z^8 a^{-8} -12 z^8 a^{-10} +10 z^8 a^{-12} -14 z^7 a^{-5} -21 z^7 a^{-7} -35 z^7 a^{-9} -19 z^7 a^{-11} +9 z^7 a^{-13} -5 z^6 a^{-4} +21 z^6 a^{-6} +55 z^6 a^{-8} +5 z^6 a^{-10} -18 z^6 a^{-12} +6 z^6 a^{-14} +19 z^5 a^{-5} +38 z^5 a^{-7} +49 z^5 a^{-9} +13 z^5 a^{-11} -14 z^5 a^{-13} +3 z^5 a^{-15} +8 z^4 a^{-4} -11 z^4 a^{-6} -43 z^4 a^{-8} -6 z^4 a^{-10} +11 z^4 a^{-12} -6 z^4 a^{-14} +z^4 a^{-16} -7 z^3 a^{-5} -25 z^3 a^{-7} -37 z^3 a^{-9} -6 z^3 a^{-11} +11 z^3 a^{-13} -2 z^3 a^{-15} -5 z^2 a^{-4} +9 z^2 a^{-6} +24 z^2 a^{-8} +5 z^2 a^{-10} -z^2 a^{-12} +3 z^2 a^{-14} -z^2 a^{-16} +9 z a^{-7} +13 z a^{-9} +z a^{-11} -3 z a^{-13} + a^{-4} -5 a^{-6} -8 a^{-8} -3 a^{-10} }[/math] |
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