K13a3671
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a3671/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -6 t^3+33 t^2-78 t+103-78 t^{-1} +33 t^{-2} -6 t^{-3} }[/math] |
| Conway polynomial | Data:K13a3671/Conway Polynomial |
| Determinant | 337 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+3 z^4 a^4+2 z^2 a^4-a^4-2 z^6 a^2-z^4 a^2+3 z^2 a^2+3 a^2-3 z^6-6 z^4-6 z^2-2-z^6 a^{-2} +z^2 a^{-2} + a^{-2} +z^4 a^{-4} +z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^2 z^{12}+3 z^{12}+9 a^3 z^{11}+19 a z^{11}+10 z^{11} a^{-1} +13 a^4 z^{10}+20 a^2 z^{10}+15 z^{10} a^{-2} +22 z^{10}+11 a^5 z^9-3 a^3 z^9-37 a z^9-9 z^9 a^{-1} +14 z^9 a^{-3} +5 a^6 z^8-26 a^4 z^8-68 a^2 z^8-36 z^8 a^{-2} +9 z^8 a^{-4} -82 z^8+a^7 z^7-28 a^5 z^7-37 a^3 z^7+11 a z^7-20 z^7 a^{-1} -35 z^7 a^{-3} +4 z^7 a^{-5} -12 a^6 z^6+4 a^4 z^6+71 a^2 z^6+40 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} +116 z^6-2 a^7 z^5+20 a^5 z^5+41 a^3 z^5+26 a z^5+51 z^5 a^{-1} +36 z^5 a^{-3} -8 z^5 a^{-5} +8 a^6 z^4+7 a^4 z^4-42 a^2 z^4-18 z^4 a^{-2} +13 z^4 a^{-4} -2 z^4 a^{-6} -74 z^4+a^7 z^3-6 a^5 z^3-17 a^3 z^3-24 a z^3-31 z^3 a^{-1} -15 z^3 a^{-3} +2 z^3 a^{-5} -2 a^6 z^2+16 a^2 z^2+5 z^2 a^{-2} -3 z^2 a^{-4} +22 z^2+a^5 z+3 a^3 z+5 a z+5 z a^{-1} +2 z a^{-3} -a^4-3 a^2- 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. |
