K13a3775
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a3775/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-14 t^3+46 t^2-91 t+115-91 t^{-1} +46 t^{-2} -14 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3775/Conway Polynomial |
| Determinant | 421 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-2 a^4 z^6+2 a^2 z^6-z^6 a^{-2} +3 z^6+a^6 z^4-4 a^4 z^4+2 a^2 z^4-2 z^4 a^{-2} +5 z^4+a^6 z^2-4 a^4 z^2+a^2 z^2-2 z^2 a^{-2} +3 z^2+a^6-2 a^4+a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^4 z^{12}+5 a^2 z^{12}+12 a^5 z^{11}+31 a^3 z^{11}+19 a z^{11}+11 a^6 z^{10}+21 a^4 z^{10}+43 a^2 z^{10}+33 z^{10}+5 a^7 z^9-26 a^5 z^9-67 a^3 z^9+36 z^9 a^{-1} +a^8 z^8-35 a^6 z^8-105 a^4 z^8-146 a^2 z^8+27 z^8 a^{-2} -50 z^8-16 a^7 z^7-2 a^5 z^7+9 a^3 z^7-79 a z^7-60 z^7 a^{-1} +14 z^7 a^{-3} -3 a^8 z^6+36 a^6 z^6+126 a^4 z^6+137 a^2 z^6-36 z^6 a^{-2} +5 z^6 a^{-4} +9 z^6+17 a^7 z^5+29 a^5 z^5+40 a^3 z^5+74 a z^5+35 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +3 a^8 z^4-15 a^6 z^4-62 a^4 z^4-59 a^2 z^4+20 z^4 a^{-2} -z^4 a^{-4} +6 z^4-7 a^7 z^3-13 a^5 z^3-18 a^3 z^3-24 a z^3-9 z^3 a^{-1} +3 z^3 a^{-3} -a^8 z^2+5 a^6 z^2+17 a^4 z^2+13 a^2 z^2-4 z^2 a^{-2} -2 z^2+a^7 z+a^5 z+a^3 z+2 a z+z a^{-1} -a^6-2 a^4-a^2+1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
