K13n15
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Polynomial invariants
| Jones polynomial | Data:K13n15/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+13 t^2-22 t+25-22 t^{-1} +13 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | Data:K13n15/Conway Polynomial |
| Determinant | 101 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -3 z^4 a^{-4} -z^4 a^{-6} -3 z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} -3 z^2 a^{-8} +3 z^2 a^{-10} +2 a^{-2} -2 a^{-4} +2 a^{-6} -2 a^{-8} +2 a^{-10} - a^{-12} }[/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} +z^9 a^{-9} +3 z^9 a^{-11} +2 z^8 a^{-4} -5 z^8 a^{-6} -20 z^8 a^{-8} -12 z^8 a^{-10} +z^8 a^{-12} +2 z^7 a^{-3} -2 z^7 a^{-5} -5 z^7 a^{-7} -11 z^7 a^{-9} -10 z^7 a^{-11} +z^6 a^{-2} -2 z^6 a^{-4} +11 z^6 a^{-6} +38 z^6 a^{-8} +26 z^6 a^{-10} +2 z^6 a^{-12} -6 z^5 a^{-3} -2 z^5 a^{-5} +15 z^5 a^{-7} +24 z^5 a^{-9} +16 z^5 a^{-11} +3 z^5 a^{-13} -4 z^4 a^{-2} -7 z^4 a^{-4} -15 z^4 a^{-6} -28 z^4 a^{-8} -28 z^4 a^{-10} -12 z^4 a^{-12} +4 z^3 a^{-3} -z^3 a^{-5} -12 z^3 a^{-7} -14 z^3 a^{-9} -15 z^3 a^{-11} -8 z^3 a^{-13} +5 z^2 a^{-2} +8 z^2 a^{-4} +8 z^2 a^{-6} +11 z^2 a^{-8} +14 z^2 a^{-10} +8 z^2 a^{-12} +z a^{-5} +3 z a^{-7} +3 z a^{-9} +4 z a^{-11} +3 z a^{-13} -2 a^{-2} -2 a^{-4} -2 a^{-6} -2 a^{-8} -2 a^{-10} - a^{-12} }[/math] |
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