K12n232
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^2-2 q+2-2 q^{-2} +5 q^{-3} -6 q^{-4} +7 q^{-5} -7 q^{-6} +5 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^2+8 t-11+8 t^{-1} -2 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-2 z^4 }[/math] |
| Determinant | 31 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-2 z^4 a^6-5 z^2 a^6-4 a^6+z^6 a^4+5 z^4 a^4+10 z^2 a^4+6 a^4-z^6 a^2-6 z^4 a^2-9 z^2 a^2-4 a^2+z^4+3 z^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-3 z^4 a^{10}+2 z^2 a^{10}+3 z^7 a^9-10 z^5 a^9+8 z^3 a^9-2 z a^9+3 z^8 a^8-8 z^6 a^8+2 z^4 a^8-z^2 a^8+a^8+z^9 a^7+2 z^7 a^7-15 z^5 a^7+12 z^3 a^7-4 z a^7+4 z^8 a^6-15 z^6 a^6+18 z^4 a^6-13 z^2 a^6+4 a^6+2 z^9 a^5-11 z^7 a^5+18 z^5 a^5-8 z^3 a^5+z^{10} a^4-5 z^8 a^4-2 z^6 a^4+26 z^4 a^4-22 z^2 a^4+6 a^4+3 z^9 a^3-23 z^7 a^3+46 z^5 a^3-26 z^3 a^3+4 z a^3+z^{10} a^2-5 z^8 a^2-2 z^6 a^2+23 z^4 a^2-19 z^2 a^2+4 a^2+2 z^9 a-13 z^7 a+23 z^5 a-14 z^3 a+2 z a+z^8-6 z^6+10 z^4-7 z^2+2 }[/math] |
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