K12a90
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-19 q^6+27 q^5-33 q^4+36 q^3-33 q^2+27 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+49 t-61+49 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +3 z^6 a^{-4} +z^6-12 z^4 a^{-2} +10 z^4 a^{-4} -3 z^4 a^{-6} +3 z^4-12 z^2 a^{-2} +13 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +4 z^2-4 a^{-2} +6 a^{-4} -4 a^{-6} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +5 z^{10} a^{-2} +10 z^{10} a^{-4} +5 z^{10} a^{-6} +9 z^9 a^{-1} +24 z^9 a^{-3} +24 z^9 a^{-5} +9 z^9 a^{-7} +14 z^8 a^{-2} +13 z^8 a^{-4} +15 z^8 a^{-6} +8 z^8 a^{-8} +8 z^8+4 a z^7-11 z^7 a^{-1} -50 z^7 a^{-3} -48 z^7 a^{-5} -9 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-53 z^6 a^{-2} -74 z^6 a^{-4} -54 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5-z^5 a^{-1} +28 z^5 a^{-3} +22 z^5 a^{-5} -7 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+56 z^4 a^{-2} +80 z^4 a^{-4} +52 z^4 a^{-6} +11 z^4 a^{-8} -2 z^4 a^{-10} +13 z^4+5 a z^3+5 z^3 a^{-1} +5 z^3 a^{-5} +11 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-26 z^2 a^{-2} -34 z^2 a^{-4} -22 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -7 z^2-a z-2 z a^{-1} -2 z a^{-3} -4 z a^{-5} -5 z a^{-7} -2 z a^{-9} +4 a^{-2} +6 a^{-4} +4 a^{-6} + a^{-8} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
