K12n86
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-13 q^6+16 q^5-17 q^4+17 q^3-13 q^2+9 q-4+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-10 t^2+24 t-31+24 t^{-1} -10 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 103 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-4} -3 z^4 a^{-2} +8 z^4 a^{-4} -3 z^4 a^{-6} -6 z^2 a^{-2} +13 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +z^2-3 a^{-2} +7 a^{-4} -5 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +7 z^9 a^{-5} +4 z^9 a^{-7} +2 z^8 a^{-2} +8 z^8 a^{-4} +12 z^8 a^{-6} +6 z^8 a^{-8} -6 z^7 a^{-3} -9 z^7 a^{-5} +z^7 a^{-7} +4 z^7 a^{-9} -4 z^6 a^{-2} -28 z^6 a^{-4} -38 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} +4 z^5 a^{-1} +11 z^5 a^{-3} -8 z^5 a^{-5} -25 z^5 a^{-7} -10 z^5 a^{-9} +14 z^4 a^{-2} +43 z^4 a^{-4} +37 z^4 a^{-6} +5 z^4 a^{-8} -2 z^4 a^{-10} +z^4-4 z^3 a^{-1} -2 z^3 a^{-3} +19 z^3 a^{-5} +24 z^3 a^{-7} +7 z^3 a^{-9} -13 z^2 a^{-2} -27 z^2 a^{-4} -19 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -2 z^2-2 z a^{-3} -8 z a^{-5} -8 z a^{-7} -2 z a^{-9} +3 a^{-2} +7 a^{-4} +5 a^{-6} + a^{-8} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
