K13a2613
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a2613/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-5 t^4+15 t^3-30 t^2+45 t-51+45 t^{-1} -30 t^{-2} +15 t^{-3} -5 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a2613/Conway Polynomial |
| Determinant | 243 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +8 z^8 a^{-2} -2 z^8 a^{-4} -z^8+28 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} -6 z^6+53 z^4 a^{-2} -33 z^4 a^{-4} +5 z^4 a^{-6} -15 z^4+53 z^2 a^{-2} -38 z^2 a^{-4} +8 z^2 a^{-6} -18 z^2+22 a^{-2} -17 a^{-4} +4 a^{-6} -8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-2} +z^{12} a^{-4} +4 z^{11} a^{-1} +8 z^{11} a^{-3} +4 z^{11} a^{-5} +15 z^{10} a^{-2} +15 z^{10} a^{-4} +7 z^{10} a^{-6} +7 z^{10}+6 a z^9+4 z^9 a^{-1} -4 z^9 a^{-3} +5 z^9 a^{-5} +7 z^9 a^{-7} +3 a^2 z^8-54 z^8 a^{-2} -51 z^8 a^{-4} -13 z^8 a^{-6} +5 z^8 a^{-8} -18 z^8+a^3 z^7-18 a z^7-42 z^7 a^{-1} -44 z^7 a^{-3} -39 z^7 a^{-5} -15 z^7 a^{-7} +3 z^7 a^{-9} -9 a^2 z^6+86 z^6 a^{-2} +80 z^6 a^{-4} +12 z^6 a^{-6} -10 z^6 a^{-8} +z^6 a^{-10} +20 z^6-4 a^3 z^5+19 a z^5+75 z^5 a^{-1} +109 z^5 a^{-3} +79 z^5 a^{-5} +14 z^5 a^{-7} -8 z^5 a^{-9} +7 a^2 z^4-92 z^4 a^{-2} -70 z^4 a^{-4} -5 z^4 a^{-6} +4 z^4 a^{-8} -3 z^4 a^{-10} -27 z^4+5 a^3 z^3-13 a z^3-71 z^3 a^{-1} -106 z^3 a^{-3} -66 z^3 a^{-5} -7 z^3 a^{-7} +6 z^3 a^{-9} -a^2 z^2+62 z^2 a^{-2} +46 z^2 a^{-4} +6 z^2 a^{-6} +2 z^2 a^{-10} +23 z^2-2 a^3 z+5 a z+26 z a^{-1} +39 z a^{-3} +23 z a^{-5} +z a^{-7} -2 z a^{-9} -22 a^{-2} -17 a^{-4} -4 a^{-6} -8 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
