K12a859
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+3 q^{-1} -4 q^{-2} +7 q^{-3} -8 q^{-4} +10 q^{-5} -11 q^{-6} +10 q^{-7} -9 q^{-8} +7 q^{-9} -5 q^{-10} +3 q^{-11} - q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+8 t^3-10 t^2+11 t-11+11 t^{-1} -10 t^{-2} +8 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+11 z^6+8 z^4+4 z^2+1 }[/math] |
| Determinant | 79 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6 z^{10}-a^8 z^8+8 a^6 z^8-a^4 z^8-6 a^8 z^6+23 a^6 z^6-6 a^4 z^6-11 a^8 z^4+29 a^6 z^4-10 a^4 z^4-7 a^8 z^2+14 a^6 z^2-3 a^4 z^2-a^8+2 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{15}+3 z^4 a^{14}-z^2 a^{14}+5 z^5 a^{13}-4 z^3 a^{13}+z a^{13}+6 z^6 a^{12}-7 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-9 z^5 a^{11}-z^3 a^{11}+z a^{11}+6 z^8 a^{10}-14 z^6 a^{10}+4 z^4 a^{10}+6 z^9 a^9-21 z^7 a^9+19 z^5 a^9-8 z^3 a^9+2 z a^9+5 z^{10} a^8-22 z^8 a^8+29 z^6 a^8-19 z^4 a^8+9 z^2 a^8-a^8+2 z^{11} a^7-4 z^9 a^7-17 z^7 a^7+42 z^5 a^7-23 z^3 a^7+2 z a^7+8 z^{10} a^6-48 z^8 a^6+93 z^6 a^6-70 z^4 a^6+19 z^2 a^6+2 z^{11} a^5-9 z^9 a^5+4 z^7 a^5+20 z^5 a^5-18 z^3 a^5+z a^5+3 z^{10} a^4-20 z^8 a^4+44 z^6 a^4-37 z^4 a^4+8 z^2 a^4+2 a^4+z^9 a^3-6 z^7 a^3+11 z^5 a^3-7 z^3 a^3+z a^3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
