K12a948
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-11 q^6+21 q^5-31 q^4+38 q^3-40 q^2+38 q-30+21 q^{-1} -11 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-29 t^2+54 t-65+54 t^{-1} -29 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 251 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-3 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +5 z^4-2 a^2 z^2-z^2 a^{-2} +4 z^2 a^{-4} -2 z^2 a^{-6} +4 z^2-a^2+ a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +20 z^{10} a^{-2} +12 z^{10} a^{-4} +8 z^{10}+8 a z^9+20 z^9 a^{-1} +31 z^9 a^{-3} +19 z^9 a^{-5} +4 a^2 z^8-30 z^8 a^{-2} +17 z^8 a^{-6} -9 z^8+a^3 z^7-20 a z^7-71 z^7 a^{-1} -91 z^7 a^{-3} -31 z^7 a^{-5} +10 z^7 a^{-7} -11 a^2 z^6-13 z^6 a^{-2} -40 z^6 a^{-4} -28 z^6 a^{-6} +4 z^6 a^{-8} -16 z^6-3 a^3 z^5+16 a z^5+70 z^5 a^{-1} +85 z^5 a^{-3} +21 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+26 z^4 a^{-2} +42 z^4 a^{-4} +25 z^4 a^{-6} -3 z^4 a^{-8} +23 z^4+3 a^3 z^3-5 a z^3-34 z^3 a^{-1} -40 z^3 a^{-3} -5 z^3 a^{-5} +8 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2-9 z^2 a^{-2} -14 z^2 a^{-4} -9 z^2 a^{-6} -9 z^2-a^3 z+a z+7 z a^{-1} +8 z a^{-3} +z a^{-5} -2 z a^{-7} +a^2+ a^{-4} + a^{-6} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
