K12a1134
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-2 q^9+3 q^8-5 q^7+6 q^6-7 q^5+7 q^4-6 q^3+6 q^2-4 q+3-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-5 t^3+7 t^2-7 t+7-7 t^{-1} +7 t^{-2} -5 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-7 z^8-16 z^6-13 z^4-z^2+1 }[/math] |
| Determinant | 53 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -9 z^8 a^{-4} +z^8 a^{-6} +7 z^6 a^{-2} -30 z^6 a^{-4} +7 z^6 a^{-6} +16 z^4 a^{-2} -45 z^4 a^{-4} +16 z^4 a^{-6} +14 z^2 a^{-2} -28 z^2 a^{-4} +13 z^2 a^{-6} +4 a^{-2} -5 a^{-4} +2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10} a^{-6} +2 z^9 a^{-1} -4 z^9 a^{-3} -4 z^9 a^{-5} +2 z^9 a^{-7} -12 z^8 a^{-2} -26 z^8 a^{-4} -11 z^8 a^{-6} +2 z^8 a^{-8} +z^8-12 z^7 a^{-1} +z^7 a^{-3} +3 z^7 a^{-5} -8 z^7 a^{-7} +2 z^7 a^{-9} +24 z^6 a^{-2} +63 z^6 a^{-4} +25 z^6 a^{-6} -6 z^6 a^{-8} +2 z^6 a^{-10} -6 z^6+21 z^5 a^{-1} +8 z^5 a^{-3} +5 z^5 a^{-5} +12 z^5 a^{-7} -4 z^5 a^{-9} +2 z^5 a^{-11} -24 z^4 a^{-2} -74 z^4 a^{-4} -28 z^4 a^{-6} +8 z^4 a^{-8} -3 z^4 a^{-10} +z^4 a^{-12} +10 z^4-11 z^3 a^{-1} -9 z^3 a^{-3} -10 z^3 a^{-5} -4 z^3 a^{-7} +4 z^3 a^{-9} -4 z^3 a^{-11} +15 z^2 a^{-2} +36 z^2 a^{-4} +13 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} -2 z^2 a^{-12} -4 z^2+z a^{-1} +3 z a^{-3} +2 z a^{-5} -z a^{-7} +z a^{-11} -4 a^{-2} -5 a^{-4} -2 a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
