K13a4468
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a4468/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+19 t^2-25 t+27-25 t^{-1} +19 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a4468/Conway Polynomial |
| Determinant | 137 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4 z^8+a^2 z^8-a^6 z^6+5 a^4 z^6+5 a^2 z^6-2 z^6-4 a^6 z^4+8 a^4 z^4+9 a^2 z^4+z^4 a^{-2} -9 z^4-4 a^6 z^2+6 a^4 z^2+9 a^2 z^2+3 z^2 a^{-2} -12 z^2-2 a^6+2 a^4+4 a^2+2 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{12}+2 z^{12}+7 a^3 z^{11}+10 a z^{11}+3 z^{11} a^{-1} +12 a^4 z^{10}+4 a^2 z^{10}+z^{10} a^{-2} -7 z^{10}+15 a^5 z^9-24 a^3 z^9-60 a z^9-21 z^9 a^{-1} +15 a^6 z^8-46 a^4 z^8-66 a^2 z^8-7 z^8 a^{-2} -12 z^8+12 a^7 z^7-53 a^5 z^7+a^3 z^7+118 a z^7+52 z^7 a^{-1} +9 a^8 z^6-44 a^6 z^6+39 a^4 z^6+146 a^2 z^6+18 z^6 a^{-2} +72 z^6+6 a^9 z^5-23 a^7 z^5+46 a^5 z^5+42 a^3 z^5-87 a z^5-54 z^5 a^{-1} +3 a^{10} z^4-11 a^8 z^4+32 a^6 z^4+2 a^4 z^4-113 a^2 z^4-21 z^4 a^{-2} -90 z^4+a^{11} z^3-4 a^9 z^3+5 a^7 z^3-10 a^5 z^3-20 a^3 z^3+21 a z^3+21 z^3 a^{-1} +a^8 z^2-12 a^6 z^2-5 a^4 z^2+35 a^2 z^2+11 z^2 a^{-2} +38 z^2+a^9 z-a^7 z-a^5 z+a^3 z-2 a z-2 z a^{-1} +2 a^6+2 a^4-4 a^2-2 a^{-2} -5 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
