K14a13086
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K14a13086/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+15 t^3-50 t^2+91 t-107+91 t^{-1} -50 t^{-2} +15 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K14a13086/Conway Polynomial |
| Determinant | Data:K14a13086/Determinant |
| Signature | Data:K14a13086/Signature |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +3 z^6-3 a^2 z^4+4 z^4 a^{-2} -10 z^4 a^{-4} +3 z^4 a^{-6} +6 z^4+a^4 z^2-6 a^2 z^2+9 z^2 a^{-2} -13 z^2 a^{-4} +4 z^2 a^{-6} -z^2+2 a^4-a^2+7 a^{-2} -5 a^{-4} +2 a^{-6} -4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +14 z^{12} $Failed^{-1} +9 z^{12} $Failed^{-1} +5 z^{12}+7 \text{QuantumGroups$\grave{ }$a} z^{11}+13 z^{11} $Failed^{-1} +25 z^{11} $Failed^{-1} +19 z^{11} $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-25 z^{10} $Failed^{-1} +4 z^{10} $Failed^{-1} +23 z^{10} $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^3 z^9-17 \text{QuantumGroups$\grave{ }$a} z^9-50 z^9 $Failed^{-1} -96 z^9 $Failed^{-1} -48 z^9 $Failed^{-1} +18 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^8-20 \text{QuantumGroups$\grave{ }$a}^2 z^8-17 z^8 $Failed^{-1} -83 z^8 $Failed^{-1} -70 z^8 $Failed^{-1} +10 z^8 $Failed^{-1} -35 z^8-11 \text{QuantumGroups$\grave{ }$a}^3 z^7+10 \text{QuantumGroups$\grave{ }$a} z^7+66 z^7 $Failed^{-1} +139 z^7 $Failed^{-1} +42 z^7 $Failed^{-1} -48 z^7 $Failed^{-1} +4 z^7 $Failed^{-1} -5 \text{QuantumGroups$\grave{ }$a}^4 z^6+21 \text{QuantumGroups$\grave{ }$a}^2 z^6+94 z^6 $Failed^{-1} +177 z^6 $Failed^{-1} +94 z^6 $Failed^{-1} -21 z^6 $Failed^{-1} +z^6 $Failed^{-1} +59 z^6+12 \text{QuantumGroups$\grave{ }$a}^3 z^5-13 \text{QuantumGroups$\grave{ }$a} z^5-67 z^5 $Failed^{-1} -88 z^5 $Failed^{-1} +11 z^5 $Failed^{-1} +50 z^5 $Failed^{-1} -7 z^5 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^4 z^4-9 \text{QuantumGroups$\grave{ }$a}^2 z^4-126 z^4 $Failed^{-1} -150 z^4 $Failed^{-1} -55 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} -62 z^4-3 \text{QuantumGroups$\grave{ }$a}^3 z^3+23 \text{QuantumGroups$\grave{ }$a} z^3+44 z^3 $Failed^{-1} +20 z^3 $Failed^{-1} -18 z^3 $Failed^{-1} -20 z^3 $Failed^{-1} -7 \text{QuantumGroups$\grave{ }$a}^4 z^2+\text{QuantumGroups$\grave{ }$a}^2 z^2+62 z^2 $Failed^{-1} +54 z^2 $Failed^{-1} +18 z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +36 z^2-\text{QuantumGroups$\grave{ }$a}^3 z-11 \text{QuantumGroups$\grave{ }$a} z-15 z $Failed^{-1} -5 z $Failed^{-1} +2 z $Failed^{-1} +2 z $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^4+\text{QuantumGroups$\grave{ }$a}^2-7 $Failed^{-1} -5 $Failed^{-1} -2 $Failed^{-1} -4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
