K12a411
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-8 q^{-1} +13 q^{-2} -18 q^{-3} +23 q^{-4} -23 q^{-5} +22 q^{-6} -18 q^{-7} +12 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+21 t^2-29 t+31-29 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+6 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-5 z^2 a^8-3 a^8+z^8 a^6+5 z^6 a^6+10 z^4 a^6+11 z^2 a^6+4 a^6+z^8 a^4+4 z^6 a^4+4 z^4 a^4+z^2 a^4-z^6 a^2-3 z^4 a^2-z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-5 z^4 a^{12}+2 z^2 a^{12}+5 z^7 a^{11}-7 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+6 z^8 a^{10}-7 z^6 a^{10}+2 z^4 a^{10}+6 z^9 a^9-8 z^7 a^9+6 z^5 a^9-4 z^3 a^9+2 z a^9+5 z^{10} a^8-9 z^8 a^8+14 z^6 a^8-17 z^4 a^8+11 z^2 a^8-3 a^8+2 z^{11} a^7+5 z^9 a^7-26 z^7 a^7+39 z^5 a^7-25 z^3 a^7+6 z a^7+11 z^{10} a^6-37 z^8 a^6+49 z^6 a^6-34 z^4 a^6+14 z^2 a^6-4 a^6+2 z^{11} a^5+6 z^9 a^5-40 z^7 a^5+54 z^5 a^5-25 z^3 a^5+3 z a^5+6 z^{10} a^4-18 z^8 a^4+11 z^6 a^4+z^4 a^4-z^2 a^4+7 z^9 a^3-26 z^7 a^3+26 z^5 a^3-8 z^3 a^3+z a^3+4 z^8 a^2-14 z^6 a^2+11 z^4 a^2-2 z^2 a^2+z^7 a-3 z^5 a+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. |
