K12a647
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{16}-4 q^{15}+8 q^{14}-14 q^{13}+20 q^{12}-23 q^{11}+23 q^{10}-22 q^9+17 q^8-11 q^7+7 q^6-2 q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-10 t^3+20 t^2-28 t+31-28 t^{-1} +20 t^{-2} -10 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^8+14 z^6+20 z^4+10 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +2 z^8 a^{-10} +6 z^6 a^{-8} +11 z^6 a^{-10} -3 z^6 a^{-12} +13 z^4 a^{-8} +19 z^4 a^{-10} -13 z^4 a^{-12} +z^4 a^{-14} +12 z^2 a^{-8} +10 z^2 a^{-10} -15 z^2 a^{-12} +3 z^2 a^{-14} +4 a^{-8} - a^{-10} -3 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +8 z^{10} a^{-12} +5 z^{10} a^{-14} +2 z^9 a^{-9} +7 z^9 a^{-11} +16 z^9 a^{-13} +11 z^9 a^{-15} +z^8 a^{-8} -11 z^8 a^{-10} -19 z^8 a^{-12} +7 z^8 a^{-14} +14 z^8 a^{-16} -8 z^7 a^{-9} -39 z^7 a^{-11} -58 z^7 a^{-13} -15 z^7 a^{-15} +12 z^7 a^{-17} -6 z^6 a^{-8} +12 z^6 a^{-10} +z^6 a^{-12} -48 z^6 a^{-14} -23 z^6 a^{-16} +8 z^6 a^{-18} +8 z^5 a^{-9} +53 z^5 a^{-11} +57 z^5 a^{-13} -6 z^5 a^{-15} -14 z^5 a^{-17} +4 z^5 a^{-19} +13 z^4 a^{-8} -5 z^4 a^{-10} +7 z^4 a^{-12} +42 z^4 a^{-14} +10 z^4 a^{-16} -6 z^4 a^{-18} +z^4 a^{-20} +2 z^3 a^{-9} -23 z^3 a^{-11} -22 z^3 a^{-13} +9 z^3 a^{-15} +4 z^3 a^{-17} -2 z^3 a^{-19} -12 z^2 a^{-8} +z^2 a^{-10} +7 z^2 a^{-12} -7 z^2 a^{-14} +z^2 a^{-18} -4 z a^{-9} +2 z a^{-13} -2 z a^{-15} +4 a^{-8} + a^{-10} -3 a^{-12} - a^{-14} }[/math] |
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