K12a1056
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+11 q^7-21 q^6+30 q^5-37 q^4+40 q^3-37 q^2+30 q-20+11 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-28 t^2+52 t-63+52 t^{-1} -28 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-8 z^4-2 z^2+1 }[/math] |
| Determinant | 247 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-7 z^4 a^{-2} -7 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-5 z^2 a^{-2} -5 z^2 a^{-4} +4 z^2 a^{-6} +4 z^2- a^{-2} - a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +18 z^{10} a^{-4} +9 z^{10} a^{-6} +12 z^9 a^{-1} +20 z^9 a^{-3} +20 z^9 a^{-5} +12 z^9 a^{-7} -3 z^8 a^{-2} -23 z^8 a^{-4} -2 z^8 a^{-6} +9 z^8 a^{-8} +9 z^8+4 a z^7-22 z^7 a^{-1} -51 z^7 a^{-3} -49 z^7 a^{-5} -20 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-20 z^6 a^{-2} -3 z^6 a^{-4} -20 z^6 a^{-6} -17 z^6 a^{-8} +z^6 a^{-10} -18 z^6-7 a z^5+17 z^5 a^{-1} +39 z^5 a^{-3} +34 z^5 a^{-5} +12 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+24 z^4 a^{-2} +8 z^4 a^{-4} +16 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} +15 z^4+3 a z^3-8 z^3 a^{-1} -12 z^3 a^{-3} -10 z^3 a^{-5} -5 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-11 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -8 z^2+z a^{-1} +2 z a^{-3} +2 z a^{-5} -z a^{-9} + a^{-2} - a^{-4} - a^{-6} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
