K12a724
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+6 q^{11}-10 q^{10}+13 q^9-16 q^8+16 q^7-14 q^6+12 q^5-8 q^4+5 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-14 t^2+19 t-21+19 t^{-1} -14 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-6 z^4+3 z^2+1 }[/math] |
| Determinant | 107 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -7 z^4 a^{-6} -8 z^4 a^{-8} +4 z^4 a^{-10} +7 z^2 a^{-4} -2 z^2 a^{-6} -6 z^2 a^{-8} +4 z^2 a^{-10} +2 a^{-4} + a^{-6} -3 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} +3 z^9 a^{-9} +5 z^9 a^{-11} +z^8 a^{-4} -7 z^8 a^{-6} -17 z^8 a^{-8} -3 z^8 a^{-10} +6 z^8 a^{-12} -10 z^7 a^{-5} -10 z^7 a^{-7} -13 z^7 a^{-9} -7 z^7 a^{-11} +6 z^7 a^{-13} -6 z^6 a^{-4} +3 z^6 a^{-6} +18 z^6 a^{-8} -3 z^6 a^{-10} -7 z^6 a^{-12} +5 z^6 a^{-14} +15 z^5 a^{-5} +11 z^5 a^{-7} +5 z^5 a^{-9} -6 z^5 a^{-13} +3 z^5 a^{-15} +12 z^4 a^{-4} +6 z^4 a^{-6} -16 z^4 a^{-8} -3 z^4 a^{-10} +z^4 a^{-12} -5 z^4 a^{-14} +z^4 a^{-16} -6 z^3 a^{-5} -2 z^3 a^{-7} +2 z^3 a^{-9} +3 z^3 a^{-11} +2 z^3 a^{-13} -3 z^3 a^{-15} -9 z^2 a^{-4} -2 z^2 a^{-6} +13 z^2 a^{-8} +4 z^2 a^{-10} +z^2 a^{-12} +2 z^2 a^{-14} -z^2 a^{-16} -z a^{-5} +z a^{-7} -3 z a^{-11} +z a^{-15} +2 a^{-4} - a^{-6} -3 a^{-8} - a^{-10} }[/math] |
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