K12a737
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +13 q^{-2} -18 q^{-3} +23 q^{-4} -26 q^{-5} +25 q^{-6} -21 q^{-7} +15 q^{-8} -9 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+21 t^2-32 t+37-32 t^{-1} +21 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+7 z^4+3 z^2+1 }[/math] |
| Determinant | 165 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-2 z^2 a^8+z^8 a^6+4 z^6 a^6+4 z^4 a^6-z^2 a^6-2 a^6+z^8 a^4+5 z^6 a^4+10 z^4 a^4+10 z^2 a^4+3 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-5 z^4 a^{12}+z^2 a^{12}+8 z^7 a^{11}-12 z^5 a^{11}+6 z^3 a^{11}-2 z a^{11}+10 z^8 a^{10}-15 z^6 a^{10}+9 z^4 a^{10}-3 z^2 a^{10}+8 z^9 a^9-5 z^7 a^9-10 z^5 a^9+13 z^3 a^9-4 z a^9+4 z^{10} a^8+8 z^8 a^8-29 z^6 a^8+24 z^4 a^8-4 z^2 a^8+z^{11} a^7+12 z^9 a^7-25 z^7 a^7+8 z^5 a^7+9 z^3 a^7-4 z a^7+7 z^{10} a^6-7 z^8 a^6-12 z^6 a^6+17 z^4 a^6-8 z^2 a^6+2 a^6+z^{11} a^5+8 z^9 a^5-25 z^7 a^5+19 z^5 a^5-4 z^3 a^5-z a^5+3 z^{10} a^4-2 z^8 a^4-14 z^6 a^4+23 z^4 a^4-16 z^2 a^4+3 a^4+4 z^9 a^3-12 z^7 a^3+10 z^5 a^3-3 z^3 a^3+z a^3+3 z^8 a^2-12 z^6 a^2+16 z^4 a^2-8 z^2 a^2+z^7 a-4 z^5 a+4 z^3 a }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
