K12a391
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-4 q^{14}+9 q^{13}-17 q^{12}+23 q^{11}-28 q^{10}+30 q^9-27 q^8+22 q^7-14 q^6+8 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 7 t^3-23 t^2+40 t-47+40 t^{-1} -23 t^{-2} +7 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 7 z^6+19 z^4+11 z^2+1 }[/math] |
| Determinant | 187 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +3 z^6 a^{-10} +3 z^4 a^{-6} +10 z^4 a^{-8} +10 z^4 a^{-10} -4 z^4 a^{-12} +2 z^2 a^{-6} +9 z^2 a^{-8} +10 z^2 a^{-10} -11 z^2 a^{-12} +z^2 a^{-14} +2 a^{-8} +4 a^{-10} -7 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-11} +2 z^{11} a^{-13} +6 z^{10} a^{-10} +12 z^{10} a^{-12} +6 z^{10} a^{-14} +7 z^9 a^{-9} +10 z^9 a^{-11} +11 z^9 a^{-13} +8 z^9 a^{-15} +6 z^8 a^{-8} -11 z^8 a^{-10} -29 z^8 a^{-12} -5 z^8 a^{-14} +7 z^8 a^{-16} +3 z^7 a^{-7} -15 z^7 a^{-9} -37 z^7 a^{-11} -35 z^7 a^{-13} -12 z^7 a^{-15} +4 z^7 a^{-17} +z^6 a^{-6} -16 z^6 a^{-8} +13 z^6 a^{-10} +42 z^6 a^{-12} -2 z^6 a^{-14} -13 z^6 a^{-16} +z^6 a^{-18} -7 z^5 a^{-7} +12 z^5 a^{-9} +55 z^5 a^{-11} +45 z^5 a^{-13} -9 z^5 a^{-17} -3 z^4 a^{-6} +17 z^4 a^{-8} -13 z^4 a^{-10} -43 z^4 a^{-12} -4 z^4 a^{-14} +4 z^4 a^{-16} -2 z^4 a^{-18} +3 z^3 a^{-7} -4 z^3 a^{-9} -36 z^3 a^{-11} -31 z^3 a^{-13} +4 z^3 a^{-15} +6 z^3 a^{-17} +2 z^2 a^{-6} -11 z^2 a^{-8} +11 z^2 a^{-10} +29 z^2 a^{-12} +5 z^2 a^{-14} +z^2 a^{-16} +z^2 a^{-18} +10 z a^{-11} +8 z a^{-13} -3 z a^{-15} -z a^{-17} +2 a^{-8} -4 a^{-10} -7 a^{-12} -2 a^{-14} }[/math] |
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