K12n15
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q-5+10 q^{-1} -15 q^{-2} +18 q^{-3} -18 q^{-4} +17 q^{-5} -13 q^{-6} +8 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-9 t^2+27 t-37+27 t^{-1} -9 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-3 z^4+1 }[/math] |
| Determinant | 111 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-2 z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^4 a^4+4 z^2 a^4+3 a^4-3 z^4 a^2-5 z^2 a^2-3 a^2+2 z^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-2 z^4 a^{10}+z^2 a^{10}+4 z^7 a^9-10 z^5 a^9+7 z^3 a^9-z a^9+6 z^8 a^8-13 z^6 a^8+6 z^4 a^8-z^2 a^8+4 z^9 a^7+z^7 a^7-21 z^5 a^7+17 z^3 a^7-4 z a^7+z^{10} a^6+12 z^8 a^6-32 z^6 a^6+23 z^4 a^6-8 z^2 a^6+a^6+7 z^9 a^5-5 z^7 a^5-13 z^5 a^5+15 z^3 a^5-4 z a^5+z^{10} a^4+9 z^8 a^4-22 z^6 a^4+24 z^4 a^4-13 z^2 a^4+3 a^4+3 z^9 a^3-z^7 a^3+z^5 a^3+z^3 a^3+3 z^8 a^2-4 z^6 a^2+12 z^4 a^2-12 z^2 a^2+3 a^2+z^7 a+3 z^5 a-4 z^3 a+z a+3 z^4-5 z^2+2 }[/math] |
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