K12a877
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-3 q^{14}+6 q^{13}-11 q^{12}+15 q^{11}-19 q^{10}+20 q^9-19 q^8+16 q^7-10 q^6+7 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^3-18 t^2+27 t-29+27 t^{-1} -18 t^{-2} +6 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^6+18 z^4+9 z^2+1 }[/math] |
| Determinant | 131 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +2 z^6 a^{-10} +3 z^4 a^{-6} +12 z^4 a^{-8} +6 z^4 a^{-10} -3 z^4 a^{-12} +z^2 a^{-6} +13 z^2 a^{-8} +3 z^2 a^{-10} -9 z^2 a^{-12} +z^2 a^{-14} +4 a^{-8} -5 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +4 z^{10} a^{-10} +7 z^{10} a^{-12} +3 z^{10} a^{-14} +6 z^9 a^{-9} +8 z^9 a^{-11} +6 z^9 a^{-13} +4 z^9 a^{-15} +6 z^8 a^{-8} -8 z^8 a^{-10} -23 z^8 a^{-12} -5 z^8 a^{-14} +4 z^8 a^{-16} +3 z^7 a^{-7} -18 z^7 a^{-9} -39 z^7 a^{-11} -29 z^7 a^{-13} -8 z^7 a^{-15} +3 z^7 a^{-17} +z^6 a^{-6} -21 z^6 a^{-8} -z^6 a^{-10} +37 z^6 a^{-12} +6 z^6 a^{-14} -9 z^6 a^{-16} +z^6 a^{-18} -8 z^5 a^{-7} +15 z^5 a^{-9} +67 z^5 a^{-11} +59 z^5 a^{-13} +6 z^5 a^{-15} -9 z^5 a^{-17} -3 z^4 a^{-6} +24 z^4 a^{-8} +13 z^4 a^{-10} -27 z^4 a^{-12} -7 z^4 a^{-14} +3 z^4 a^{-16} -3 z^4 a^{-18} +2 z^3 a^{-7} -z^3 a^{-9} -42 z^3 a^{-11} -53 z^3 a^{-13} -7 z^3 a^{-15} +7 z^3 a^{-17} +z^2 a^{-6} -15 z^2 a^{-8} -4 z^2 a^{-10} +15 z^2 a^{-12} +2 z^2 a^{-14} +z^2 a^{-16} +2 z^2 a^{-18} -2 z a^{-9} +10 z a^{-11} +16 z a^{-13} +3 z a^{-15} -z a^{-17} +4 a^{-8} -5 a^{-12} -2 a^{-14} }[/math] |
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