K13a1942
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Polynomial invariants
| Jones polynomial | Data:K13a1942/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 6 t^3-18 t^2+29 t-33+29 t^{-1} -18 t^{-2} +6 t^{-3} }[/math] |
| Conway polynomial | Data:K13a1942/Conway Polynomial |
| Determinant | 139 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +2 z^6 a^{-8} +2 z^6 a^{-10} +z^6 a^{-12} +4 z^4 a^{-6} +7 z^4 a^{-8} +6 z^4 a^{-10} +2 z^4 a^{-12} -z^4 a^{-14} +4 z^2 a^{-6} +6 z^2 a^{-8} +4 z^2 a^{-10} -z^2 a^{-12} -2 z^2 a^{-14} + a^{-6} + a^{-8} + a^{-10} -2 a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-12} +z^{12} a^{-14} +2 z^{11} a^{-11} +5 z^{11} a^{-13} +3 z^{11} a^{-15} +3 z^{10} a^{-10} +z^{10} a^{-14} +4 z^{10} a^{-16} +3 z^9 a^{-9} -4 z^9 a^{-11} -22 z^9 a^{-13} -11 z^9 a^{-15} +4 z^9 a^{-17} +3 z^8 a^{-8} -9 z^8 a^{-10} -9 z^8 a^{-12} -14 z^8 a^{-14} -14 z^8 a^{-16} +3 z^8 a^{-18} +2 z^7 a^{-7} -7 z^7 a^{-9} +43 z^7 a^{-13} +19 z^7 a^{-15} -14 z^7 a^{-17} +z^7 a^{-19} +z^6 a^{-6} -9 z^6 a^{-8} +13 z^6 a^{-10} +27 z^6 a^{-12} +32 z^6 a^{-14} +16 z^6 a^{-16} -12 z^6 a^{-18} -6 z^5 a^{-7} +3 z^5 a^{-9} +12 z^5 a^{-11} -33 z^5 a^{-13} -21 z^5 a^{-15} +11 z^5 a^{-17} -4 z^5 a^{-19} -4 z^4 a^{-6} +8 z^4 a^{-8} -9 z^4 a^{-10} -25 z^4 a^{-12} -28 z^4 a^{-14} -12 z^4 a^{-16} +12 z^4 a^{-18} +3 z^3 a^{-7} +2 z^3 a^{-9} -7 z^3 a^{-11} +7 z^3 a^{-13} +8 z^3 a^{-15} -z^3 a^{-17} +4 z^3 a^{-19} +4 z^2 a^{-6} -5 z^2 a^{-8} +5 z^2 a^{-10} +13 z^2 a^{-12} +5 z^2 a^{-14} +4 z^2 a^{-16} -2 z^2 a^{-18} -2 z a^{-9} +2 z a^{-11} +z a^{-13} -2 z a^{-15} -z a^{-19} - a^{-6} + a^{-8} - a^{-10} -2 a^{-12} }[/math] |
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