K12a633
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+5 q^9-12 q^8+19 q^7-27 q^6+33 q^5-34 q^4+32 q^3-25 q^2+17 q-9+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-21 t^2+51 t-67+51 t^{-1} -21 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+3 z^4+3 z^2+1 }[/math] |
| Determinant | 219 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-8} -z^4+z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} -z^2+3 a^{-4} -2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +8 z^{10} a^{-4} +17 z^{10} a^{-6} +9 z^{10} a^{-8} +11 z^9 a^{-3} +15 z^9 a^{-5} +14 z^9 a^{-7} +10 z^9 a^{-9} +11 z^8 a^{-2} -34 z^8 a^{-6} -18 z^8 a^{-8} +5 z^8 a^{-10} +8 z^7 a^{-1} -9 z^7 a^{-3} -43 z^7 a^{-5} -56 z^7 a^{-7} -29 z^7 a^{-9} +z^7 a^{-11} -13 z^6 a^{-2} -22 z^6 a^{-4} +7 z^6 a^{-6} -z^6 a^{-8} -13 z^6 a^{-10} +4 z^6+a z^5-10 z^5 a^{-1} -7 z^5 a^{-3} +26 z^5 a^{-5} +46 z^5 a^{-7} +22 z^5 a^{-9} -2 z^5 a^{-11} +5 z^4 a^{-2} +23 z^4 a^{-4} +15 z^4 a^{-6} +10 z^4 a^{-8} +8 z^4 a^{-10} -5 z^4-a z^3+5 z^3 a^{-1} +11 z^3 a^{-3} +3 z^3 a^{-5} -7 z^3 a^{-7} -4 z^3 a^{-9} +z^3 a^{-11} -11 z^2 a^{-4} -10 z^2 a^{-6} -2 z^2 a^{-8} -z^2 a^{-10} +2 z^2-z a^{-1} -3 z a^{-3} -5 z a^{-5} -2 z a^{-7} +z a^{-9} +3 a^{-4} +2 a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
