K12a915
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+13 q^7-24 q^6+34 q^5-41 q^4+44 q^3-40 q^2+32 q-21+11 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-23 t^2+65 t-89+65 t^{-1} -23 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-5 z^4+1 }[/math] |
| Determinant | 271 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -3 z^4 a^{-2} +3 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-6 z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} +z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-3} +4 z^{11} a^{-5} +11 z^{10} a^{-2} +24 z^{10} a^{-4} +13 z^{10} a^{-6} +13 z^9 a^{-1} +23 z^9 a^{-3} +27 z^9 a^{-5} +17 z^9 a^{-7} -9 z^8 a^{-2} -40 z^8 a^{-4} -10 z^8 a^{-6} +12 z^8 a^{-8} +9 z^8+4 a z^7-25 z^7 a^{-1} -73 z^7 a^{-3} -81 z^7 a^{-5} -32 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-14 z^6 a^{-2} +7 z^6 a^{-4} -19 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -17 z^6-7 a z^5+23 z^5 a^{-1} +79 z^5 a^{-3} +76 z^5 a^{-5} +20 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+27 z^4 a^{-2} +21 z^4 a^{-4} +21 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +13 z^4+3 a z^3-14 z^3 a^{-1} -38 z^3 a^{-3} -31 z^3 a^{-5} -8 z^3 a^{-7} +2 z^3 a^{-9} +a^2 z^2-17 z^2 a^{-2} -13 z^2 a^{-4} -7 z^2 a^{-6} -3 z^2 a^{-8} -7 z^2+3 z a^{-1} +7 z a^{-3} +5 z a^{-5} +z a^{-7} +3 a^{-2} +3 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. |
