K13a4641
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a4641/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+35 t^2-64 t+79-64 t^{-1} +35 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a4641/Conway Polynomial |
| Determinant | 305 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-2 a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +3 z^6+a^4 z^4-6 a^2 z^4+8 z^4 a^{-2} -3 z^4 a^{-4} +3 z^4+2 a^4 z^2-6 a^2 z^2+9 z^2 a^{-2} -4 z^2 a^{-4} -z^2+a^4-a^2+5 a^{-2} -2 a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12}+8 a z^{11}+18 z^{11} a^{-1} +10 z^{11} a^{-3} +11 a^2 z^{10}+17 z^{10} a^{-2} +13 z^{10} a^{-4} +15 z^{10}+11 a^3 z^9-4 a z^9-46 z^9 a^{-1} -22 z^9 a^{-3} +9 z^9 a^{-5} +8 a^4 z^8-16 a^2 z^8-83 z^8 a^{-2} -43 z^8 a^{-4} +4 z^8 a^{-6} -60 z^8+4 a^5 z^7-20 a^3 z^7-23 a z^7+34 z^7 a^{-1} +5 z^7 a^{-3} -27 z^7 a^{-5} +z^7 a^{-7} +a^6 z^6-15 a^4 z^6+3 a^2 z^6+129 z^6 a^{-2} +56 z^6 a^{-4} -11 z^6 a^{-6} +81 z^6-8 a^5 z^5+14 a^3 z^5+44 a z^5+14 z^5 a^{-1} +20 z^5 a^{-3} +25 z^5 a^{-5} -3 z^5 a^{-7} -2 a^6 z^4+8 a^4 z^4+7 a^2 z^4-92 z^4 a^{-2} -46 z^4 a^{-4} +6 z^4 a^{-6} -43 z^4+4 a^5 z^3-10 a^3 z^3-28 a z^3-20 z^3 a^{-1} -22 z^3 a^{-3} -14 z^3 a^{-5} +2 z^3 a^{-7} +a^6 z^2-3 a^4 z^2-7 a^2 z^2+33 z^2 a^{-2} +17 z^2 a^{-4} +13 z^2+3 a^3 z+6 a z+6 z a^{-1} +6 z a^{-3} +3 z a^{-5} +a^4+a^2-5 a^{-2} -2 a^{-4} -2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
