K12a129
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+13 q^5-19 q^4+23 q^3-24 q^2+23 q-18+13 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-19 t^2+32 t-37+32 t^{-1} -19 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+3 z^4+3 z^2+1 }[/math] |
| Determinant | 155 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-11 z^4 a^{-2} +8 z^4 a^{-4} -z^4 a^{-6} +8 z^4-3 a^2 z^2-13 z^2 a^{-2} +11 z^2 a^{-4} -3 z^2 a^{-6} +11 z^2-2 a^2-6 a^{-2} +5 a^{-4} -2 a^{-6} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +4 z^{10} a^{-4} +3 z^{10}+4 a z^9+9 z^9 a^{-1} +12 z^9 a^{-3} +7 z^9 a^{-5} +3 a^2 z^8-7 z^8 a^{-2} +3 z^8 a^{-4} +7 z^8 a^{-6} +a^3 z^7-10 a z^7-31 z^7 a^{-1} -36 z^7 a^{-3} -11 z^7 a^{-5} +5 z^7 a^{-7} -11 a^2 z^6-22 z^6 a^{-2} -24 z^6 a^{-4} -11 z^6 a^{-6} +3 z^6 a^{-8} -23 z^6-4 a^3 z^5+2 a z^5+27 z^5 a^{-1} +38 z^5 a^{-3} +10 z^5 a^{-5} -6 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+42 z^4 a^{-2} +37 z^4 a^{-4} +10 z^4 a^{-6} -5 z^4 a^{-8} +33 z^4+5 a^3 z^3+6 a z^3-9 z^3 a^{-1} -16 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} -2 z^3 a^{-9} -7 a^2 z^2-28 z^2 a^{-2} -22 z^2 a^{-4} -6 z^2 a^{-6} +2 z^2 a^{-8} -21 z^2-2 a^3 z-3 a z+2 z a^{-3} +z a^{-9} +2 a^2+6 a^{-2} +5 a^{-4} +2 a^{-6} +6 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
