K14a6972
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K14a6972/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+9 t^4-37 t^3+92 t^2-155 t+185-155 t^{-1} +92 t^{-2} -37 t^{-3} +9 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K14a6972/Conway Polynomial |
| Determinant | Data:K14a6972/Determinant |
| Signature | Data:K14a6972/Signature |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+2 a^2 z^8+2 z^8 a^{-2} -5 z^8-a^4 z^6+7 a^2 z^6+7 z^6 a^{-2} -z^6 a^{-4} -12 z^6-2 a^4 z^4+9 a^2 z^4+9 z^4 a^{-2} -2 z^4 a^{-4} -14 z^4-a^4 z^2+4 a^2 z^2+4 z^2 a^{-2} -z^2 a^{-4} -7 z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 \text{QuantumGroups$\grave{ }$a} z^{13}+4 z^{13} $Failed^{-1} +17 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+17 z^{12} $Failed^{-1} +34 z^{12}+30 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+68 \text{QuantumGroups$\grave{ }$a} z^{11}+68 z^{11} $Failed^{-1} +30 z^{11} $Failed^{-1} +29 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+33 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+33 z^{10} $Failed^{-1} +29 z^{10} $Failed^{-1} +8 z^{10}+17 \text{QuantumGroups$\grave{ }$a}^5 z^9-39 \text{QuantumGroups$\grave{ }$a}^3 z^9-161 \text{QuantumGroups$\grave{ }$a} z^9-161 z^9 $Failed^{-1} -39 z^9 $Failed^{-1} +17 z^9 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^6 z^8-58 \text{QuantumGroups$\grave{ }$a}^4 z^8-152 \text{QuantumGroups$\grave{ }$a}^2 z^8-152 z^8 $Failed^{-1} -58 z^8 $Failed^{-1} +6 z^8 $Failed^{-1} -176 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-32 \text{QuantumGroups$\grave{ }$a}^5 z^7-8 \text{QuantumGroups$\grave{ }$a}^3 z^7+109 \text{QuantumGroups$\grave{ }$a} z^7+109 z^7 $Failed^{-1} -8 z^7 $Failed^{-1} -32 z^7 $Failed^{-1} +z^7 $Failed^{-1} -9 \text{QuantumGroups$\grave{ }$a}^6 z^6+43 \text{QuantumGroups$\grave{ }$a}^4 z^6+160 \text{QuantumGroups$\grave{ }$a}^2 z^6+160 z^6 $Failed^{-1} +43 z^6 $Failed^{-1} -9 z^6 $Failed^{-1} +216 z^6-\text{QuantumGroups$\grave{ }$a}^7 z^5+20 \text{QuantumGroups$\grave{ }$a}^5 z^5+26 \text{QuantumGroups$\grave{ }$a}^3 z^5-22 \text{QuantumGroups$\grave{ }$a} z^5-22 z^5 $Failed^{-1} +26 z^5 $Failed^{-1} +20 z^5 $Failed^{-1} -z^5 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^6 z^4-15 \text{QuantumGroups$\grave{ }$a}^4 z^4-70 \text{QuantumGroups$\grave{ }$a}^2 z^4-70 z^4 $Failed^{-1} -15 z^4 $Failed^{-1} +3 z^4 $Failed^{-1} -104 z^4-4 \text{QuantumGroups$\grave{ }$a}^5 z^3-7 \text{QuantumGroups$\grave{ }$a}^3 z^3-7 z^3 $Failed^{-1} -4 z^3 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^4 z^2+13 \text{QuantumGroups$\grave{ }$a}^2 z^2+13 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} +20 z^2-\text{QuantumGroups$\grave{ }$a} z-z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} -1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
