K12a750
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-2 q^{10}+5 q^9-11 q^8+14 q^7-19 q^6+22 q^5-19 q^4+18 q^3-13 q^2+7 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -8 t^2+34 t-51+34 t^{-1} -8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -8 z^4+2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -3 z^4 a^{-4} -3 z^4 a^{-6} -z^4 a^{-8} +2 z^2 a^{-2} -2 z^2 a^{-6} +z^2 a^{-10} +z^2+3 a^{-4} - a^{-6} -2 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +4 z^{10} a^{-6} +6 z^{10} a^{-8} +2 z^{10} a^{-10} +9 z^9 a^{-5} +10 z^9 a^{-7} +3 z^9 a^{-9} +2 z^9 a^{-11} +12 z^8 a^{-4} +6 z^8 a^{-6} -12 z^8 a^{-8} -5 z^8 a^{-10} +z^8 a^{-12} +10 z^7 a^{-3} -14 z^7 a^{-5} -36 z^7 a^{-7} -22 z^7 a^{-9} -10 z^7 a^{-11} +6 z^6 a^{-2} -26 z^6 a^{-4} -46 z^6 a^{-6} -13 z^6 a^{-8} -5 z^6 a^{-10} -6 z^6 a^{-12} +3 z^5 a^{-1} -16 z^5 a^{-3} -z^5 a^{-5} +34 z^5 a^{-7} +34 z^5 a^{-9} +18 z^5 a^{-11} -5 z^4 a^{-2} +27 z^4 a^{-4} +61 z^4 a^{-6} +36 z^4 a^{-8} +20 z^4 a^{-10} +12 z^4 a^{-12} +z^4-2 z^3 a^{-1} +12 z^3 a^{-3} +5 z^3 a^{-5} -24 z^3 a^{-7} -31 z^3 a^{-9} -16 z^3 a^{-11} +2 z^2 a^{-2} -15 z^2 a^{-4} -35 z^2 a^{-6} -21 z^2 a^{-8} -12 z^2 a^{-10} -8 z^2 a^{-12} -z^2+2 z a^{-5} +14 z a^{-7} +20 z a^{-9} +8 z a^{-11} +3 a^{-4} + a^{-6} -2 a^{-8} - a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
