K12a931
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+8 q^{10}-15 q^9+21 q^8-27 q^7+28 q^6-26 q^5+22 q^4-14 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+19 t^2-40 t+51-40 t^{-1} +19 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-5 z^4+1 }[/math] |
| Determinant | 177 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -4 z^4 a^{-6} -2 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +z^2 a^{-4} -z^2 a^{-6} -4 z^2 a^{-8} +2 z^2 a^{-10} + a^{-2} + a^{-4} + a^{-6} -4 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +5 z^{10} a^{-6} +11 z^{10} a^{-8} +6 z^{10} a^{-10} +6 z^9 a^{-5} +7 z^9 a^{-7} +9 z^9 a^{-9} +8 z^9 a^{-11} +5 z^8 a^{-4} -5 z^8 a^{-6} -26 z^8 a^{-8} -10 z^8 a^{-10} +6 z^8 a^{-12} +3 z^7 a^{-3} -9 z^7 a^{-5} -22 z^7 a^{-7} -35 z^7 a^{-9} -22 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -9 z^6 a^{-4} +31 z^6 a^{-8} +5 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +2 z^5 a^{-5} +26 z^5 a^{-7} +54 z^5 a^{-9} +30 z^5 a^{-11} -7 z^5 a^{-13} -3 z^4 a^{-2} +3 z^4 a^{-4} -19 z^4 a^{-8} +3 z^4 a^{-10} +13 z^4 a^{-12} -3 z^4 a^{-14} +4 z^3 a^{-3} +z^3 a^{-5} -15 z^3 a^{-7} -40 z^3 a^{-9} -25 z^3 a^{-11} +3 z^3 a^{-13} +3 z^2 a^{-2} -z^2 a^{-4} +10 z^2 a^{-8} -2 z^2 a^{-10} -6 z^2 a^{-12} +2 z^2 a^{-14} -2 z a^{-5} +4 z a^{-7} +14 z a^{-9} +8 z a^{-11} - a^{-2} + a^{-4} - a^{-6} -4 a^{-8} -2 a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
