K12a1191
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^2-4 q+8-12 q^{-1} +18 q^{-2} -21 q^{-3} +23 q^{-4} -22 q^{-5} +18 q^{-6} -13 q^{-7} +8 q^{-8} -4 q^{-9} + q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-12 t^3+20 t^2-25 t+27-25 t^{-1} +20 t^{-2} -12 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-7 z^6-2 z^4+2 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^{10}+a^6 z^8-7 a^4 z^8+a^2 z^8+5 a^6 z^6-17 a^4 z^6+5 a^2 z^6+7 a^6 z^4-16 a^4 z^4+7 a^2 z^4+2 a^6 z^2-3 a^4 z^2+3 a^2 z^2-a^6+a^4+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^4 a^{12}+4 z^5 a^{11}-2 z^3 a^{11}+8 z^6 a^{10}-7 z^4 a^{10}+z^2 a^{10}+11 z^7 a^9-13 z^5 a^9+3 z^3 a^9+12 z^8 a^8-18 z^6 a^8+4 z^4 a^8+z^2 a^8+11 z^9 a^7-21 z^7 a^7+7 z^5 a^7+z^3 a^7-z a^7+8 z^{10} a^6-17 z^8 a^6+5 z^6 a^6+a^6+3 z^{11} a^5+4 z^9 a^5-41 z^7 a^5+51 z^5 a^5-19 z^3 a^5+z a^5+14 z^{10} a^4-57 z^8 a^4+71 z^6 a^4-32 z^4 a^4+3 z^2 a^4+a^4+3 z^{11} a^3-3 z^9 a^3-27 z^7 a^3+50 z^5 a^3-24 z^3 a^3+3 z a^3+6 z^{10} a^2-27 z^8 a^2+36 z^6 a^2-16 z^4 a^2+2 z^2 a^2-a^2+4 z^9 a-18 z^7 a+23 z^5 a-9 z^3 a+z a+z^8-4 z^6+4 z^4-z^2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
