K12a967
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 1-4 q^{-1} +11 q^{-2} -20 q^{-3} +30 q^{-4} -37 q^{-5} +41 q^{-6} -38 q^{-7} +31 q^{-8} -22 q^{-9} +12 q^{-10} -5 q^{-11} + q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+27 t^2-58 t+73-58 t^{-1} +27 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-3 z^4+5 z^2+1 }[/math] |
| Determinant | 253 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^{10}-a^{10}-z^6 a^8+z^4 a^8+4 z^2 a^8+a^8-3 z^6 a^6-7 z^4 a^6-5 z^2 a^6-a^6-z^6 a^4+z^4 a^4+5 z^2 a^4+2 a^4+z^4 a^2+z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{14}-z^4 a^{14}+5 z^7 a^{13}-8 z^5 a^{13}+2 z^3 a^{13}+z a^{13}+11 z^8 a^{12}-20 z^6 a^{12}+8 z^4 a^{12}-z^2 a^{12}+15 z^9 a^{11}-30 z^7 a^{11}+21 z^5 a^{11}-11 z^3 a^{11}+z a^{11}+12 z^{10} a^{10}-15 z^8 a^{10}-3 z^6 a^{10}+8 z^4 a^{10}-5 z^2 a^{10}+a^{10}+4 z^{11} a^9+21 z^9 a^9-74 z^7 a^9+83 z^5 a^9-38 z^3 a^9+6 z a^9+23 z^{10} a^8-49 z^8 a^8+30 z^6 a^8+7 z^4 a^8-6 z^2 a^8+a^8+4 z^{11} a^7+19 z^9 a^7-71 z^7 a^7+86 z^5 a^7-41 z^3 a^7+8 z a^7+11 z^{10} a^6-14 z^8 a^6-7 z^6 a^6+23 z^4 a^6-12 z^2 a^6+a^6+13 z^9 a^5-28 z^7 a^5+25 z^5 a^5-14 z^3 a^5+2 z a^5+9 z^8 a^4-18 z^6 a^4+13 z^4 a^4-9 z^2 a^4+2 a^4+4 z^7 a^3-7 z^5 a^3+2 z^3 a^3+z^6 a^2-2 z^4 a^2+z^2 a^2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
