K13n4012
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n4012/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-19 t^2+32 t-37+32 t^{-1} -19 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | Data:K13n4012/Conway Polynomial |
| Determinant | 155 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8+3 a^2 z^6+z^6 a^{-2} -5 z^6-2 a^4 z^4+12 a^2 z^4+3 z^4 a^{-2} -10 z^4-5 a^4 z^2+15 a^2 z^2+2 z^2 a^{-2} -9 z^2-3 a^4+6 a^2-2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +8 a^2 z^{10}+6 z^{10} a^{-2} +14 z^{10}+10 a^3 z^9+4 a z^9-2 z^9 a^{-1} +4 z^9 a^{-3} +8 a^4 z^8-18 a^2 z^8-26 z^8 a^{-2} +z^8 a^{-4} -53 z^8+4 a^5 z^7-20 a^3 z^7-32 a z^7-26 z^7 a^{-1} -18 z^7 a^{-3} +a^6 z^6-8 a^4 z^6+19 a^2 z^6+36 z^6 a^{-2} -4 z^6 a^{-4} +68 z^6+3 a^5 z^5+15 a^3 z^5+31 a z^5+44 z^5 a^{-1} +25 z^5 a^{-3} +6 a^6 z^4-3 a^4 z^4-34 a^2 z^4-19 z^4 a^{-2} +4 z^4 a^{-4} -48 z^4+3 a^7 z^3-4 a^5 z^3-14 a^3 z^3-17 a z^3-20 z^3 a^{-1} -10 z^3 a^{-3} -2 a^6 z^2+8 a^4 z^2+24 a^2 z^2+5 z^2 a^{-2} +19 z^2-a^7 z+2 a^5 z+6 a^3 z+5 a z+2 z a^{-1} -3 a^4-6 a^2-2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
