K12a1071
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{ -2 t^4+10 t^3-26 t^2+46 t-55+46 t^{-1} -26 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-6 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -6 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-3 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +17 z^{10} a^{-4} +8 z^{10} a^{-6} +12 z^9 a^{-1} +15 z^9 a^{-3} +13 z^9 a^{-5} +10 z^9 a^{-7} -12 z^8 a^{-2} -36 z^8 a^{-4} -7 z^8 a^{-6} +8 z^8 a^{-8} +9 z^8+4 a z^7-30 z^7 a^{-1} -52 z^7 a^{-3} -38 z^7 a^{-5} -16 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-4 z^6 a^{-2} +33 z^6 a^{-4} -2 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -22 z^6-8 a z^5+30 z^5 a^{-1} +61 z^5 a^{-3} +37 z^5 a^{-5} +6 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+17 z^4 a^{-2} -16 z^4 a^{-4} -3 z^4 a^{-6} +8 z^4 a^{-8} -2 z^4 a^{-10} +18 z^4+2 a z^3-13 z^3 a^{-1} -28 z^3 a^{-3} -19 z^3 a^{-5} -z^3 a^{-7} +5 z^3 a^{-9} -7 z^2 a^{-2} +4 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} -7 z^2+2 z a^{-1} +5 z a^{-3} +3 z a^{-5} -z a^{-7} -z a^{-9} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
