K12n822
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+4 q^7-7 q^6+8 q^5-9 q^4+9 q^3-7 q^2+5 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+3 t^3-6 t^2+11 t-13+11 t^{-1} -6 t^{-2} +3 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-5 z^6-8 z^4-2 z^2+1 }[/math] |
| Determinant | 55 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-4} +z^6 a^{-2} -7 z^6 a^{-4} +z^6 a^{-6} +5 z^4 a^{-2} -18 z^4 a^{-4} +5 z^4 a^{-6} +9 z^2 a^{-2} -19 z^2 a^{-4} +8 z^2 a^{-6} +5 a^{-2} -7 a^{-4} +3 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +3 z^9 a^{-5} +2 z^9 a^{-7} -5 z^8 a^{-4} -3 z^8 a^{-6} +2 z^8 a^{-8} -3 z^7 a^{-3} -12 z^7 a^{-5} -7 z^7 a^{-7} +2 z^7 a^{-9} +4 z^6 a^{-2} +18 z^6 a^{-4} +8 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +2 z^5 a^{-1} +7 z^5 a^{-3} +25 z^5 a^{-5} +13 z^5 a^{-7} -7 z^5 a^{-9} -10 z^4 a^{-2} -29 z^4 a^{-4} -12 z^4 a^{-6} +2 z^4 a^{-8} -4 z^4 a^{-10} +z^4-3 z^3 a^{-1} -4 z^3 a^{-3} -22 z^3 a^{-5} -15 z^3 a^{-7} +6 z^3 a^{-9} +12 z^2 a^{-2} +26 z^2 a^{-4} +7 z^2 a^{-6} -z^2 a^{-8} +4 z^2 a^{-10} -2 z^2+3 z a^{-3} +7 z a^{-5} +3 z a^{-7} -z a^{-9} -5 a^{-2} -7 a^{-4} -3 a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
