K14a13712
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K14a13712/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-8 t^4+32 t^3-79 t^2+132 t-155+132 t^{-1} -79 t^{-2} +32 t^{-3} -8 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K14a13712/Conway Polynomial |
| Determinant | Data:K14a13712/Determinant |
| Signature | Data:K14a13712/Signature |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +6 z^8 a^{-2} -z^8 a^{-4} -3 z^8+3 a^2 z^6+16 z^6 a^{-2} -4 z^6 a^{-4} -12 z^6-a^4 z^4+7 a^2 z^4+19 z^4 a^{-2} -6 z^4 a^{-4} -16 z^4-a^4 z^2+3 a^2 z^2+7 z^2 a^{-2} -3 z^2 a^{-4} -5 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 7 \text{QuantumGroups$\grave{ }$a} z^{13}+7 z^{13} $Failed^{-1} +17 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+28 z^{12} $Failed^{-1} +45 z^{12}+15 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+29 \text{QuantumGroups$\grave{ }$a} z^{11}+65 z^{11} $Failed^{-1} +51 z^{11} $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-46 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-8 z^{10} $Failed^{-1} +58 z^{10} $Failed^{-1} -118 z^{10}+\text{QuantumGroups$\grave{ }$a}^5 z^9-56 \text{QuantumGroups$\grave{ }$a}^3 z^9-186 \text{QuantumGroups$\grave{ }$a} z^9-282 z^9 $Failed^{-1} -106 z^9 $Failed^{-1} +47 z^9 $Failed^{-1} -21 \text{QuantumGroups$\grave{ }$a}^4 z^8+4 \text{QuantumGroups$\grave{ }$a}^2 z^8-173 z^8 $Failed^{-1} -128 z^8 $Failed^{-1} +29 z^8 $Failed^{-1} +9 z^8-3 \text{QuantumGroups$\grave{ }$a}^5 z^7+69 \text{QuantumGroups$\grave{ }$a}^3 z^7+269 \text{QuantumGroups$\grave{ }$a} z^7+330 z^7 $Failed^{-1} +36 z^7 $Failed^{-1} -83 z^7 $Failed^{-1} +14 z^7 $Failed^{-1} +25 \text{QuantumGroups$\grave{ }$a}^4 z^6+67 \text{QuantumGroups$\grave{ }$a}^2 z^6+245 z^6 $Failed^{-1} +95 z^6 $Failed^{-1} -33 z^6 $Failed^{-1} +5 z^6 $Failed^{-1} +154 z^6+3 \text{QuantumGroups$\grave{ }$a}^5 z^5-34 \text{QuantumGroups$\grave{ }$a}^3 z^5-145 \text{QuantumGroups$\grave{ }$a} z^5-150 z^5 $Failed^{-1} +16 z^5 $Failed^{-1} +49 z^5 $Failed^{-1} -8 z^5 $Failed^{-1} +z^5 $Failed^{-1} -13 \text{QuantumGroups$\grave{ }$a}^4 z^4-50 \text{QuantumGroups$\grave{ }$a}^2 z^4-123 z^4 $Failed^{-1} -38 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} -z^4 $Failed^{-1} -110 z^4-\text{QuantumGroups$\grave{ }$a}^5 z^3+9 \text{QuantumGroups$\grave{ }$a}^3 z^3+33 \text{QuantumGroups$\grave{ }$a} z^3+30 z^3 $Failed^{-1} -4 z^3 $Failed^{-1} -10 z^3 $Failed^{-1} +z^3 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^4 z^2+9 \text{QuantumGroups$\grave{ }$a}^2 z^2+21 z^2 $Failed^{-1} +9 z^2 $Failed^{-1} +18 z^2-2 \text{QuantumGroups$\grave{ }$a}^3 z-5 \text{QuantumGroups$\grave{ }$a} z-5 z $Failed^{-1} -2 z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
