K14a2858
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K14a2858/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-8 t^4+30 t^3-69 t^2+112 t-131+112 t^{-1} -69 t^{-2} +30 t^{-3} -8 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K14a2858/Conway Polynomial |
| Determinant | Data:K14a2858/Determinant |
| Signature | Data:K14a2858/Signature |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-3 a^4 z^8+6 a^2 z^8-z^8+3 a^6 z^6-14 a^4 z^6+16 a^2 z^6-4 z^6-a^8 z^4+10 a^6 z^4-24 a^4 z^4+22 a^2 z^4-6 z^4-2 a^8 z^2+10 a^6 z^2-16 a^4 z^2+15 a^2 z^2-4 z^2-a^8+2 a^6-3 a^4+4 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 \text{QuantumGroups$\grave{ }$a}^5 z^{13}+2 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+8 \text{QuantumGroups$\grave{ }$a}^6 z^{12}+18 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+10 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+15 \text{QuantumGroups$\grave{ }$a}^7 z^{11}+36 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+41 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+20 \text{QuantumGroups$\grave{ }$a} z^{11}+17 \text{QuantumGroups$\grave{ }$a}^8 z^{10}+25 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+7 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+20 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+21 z^{10}+12 \text{QuantumGroups$\grave{ }$a}^9 z^9-10 \text{QuantumGroups$\grave{ }$a}^7 z^9-83 \text{QuantumGroups$\grave{ }$a}^5 z^9-112 \text{QuantumGroups$\grave{ }$a}^3 z^9-38 \text{QuantumGroups$\grave{ }$a} z^9+13 z^9 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^{10} z^8-34 \text{QuantumGroups$\grave{ }$a}^8 z^8-98 \text{QuantumGroups$\grave{ }$a}^6 z^8-115 \text{QuantumGroups$\grave{ }$a}^4 z^8-118 \text{QuantumGroups$\grave{ }$a}^2 z^8+5 z^8 $Failed^{-1} -57 z^8+\text{QuantumGroups$\grave{ }$a}^{11} z^7-28 \text{QuantumGroups$\grave{ }$a}^9 z^7-33 \text{QuantumGroups$\grave{ }$a}^7 z^7+59 \text{QuantumGroups$\grave{ }$a}^5 z^7+108 \text{QuantumGroups$\grave{ }$a}^3 z^7+11 \text{QuantumGroups$\grave{ }$a} z^7-33 z^7 $Failed^{-1} +z^7 $Failed^{-1} -11 \text{QuantumGroups$\grave{ }$a}^{10} z^6+22 \text{QuantumGroups$\grave{ }$a}^8 z^6+112 \text{QuantumGroups$\grave{ }$a}^6 z^6+183 \text{QuantumGroups$\grave{ }$a}^4 z^6+175 \text{QuantumGroups$\grave{ }$a}^2 z^6-11 z^6 $Failed^{-1} +60 z^6-2 \text{QuantumGroups$\grave{ }$a}^{11} z^5+23 \text{QuantumGroups$\grave{ }$a}^9 z^5+42 \text{QuantumGroups$\grave{ }$a}^7 z^5-14 \text{QuantumGroups$\grave{ }$a}^5 z^5-37 \text{QuantumGroups$\grave{ }$a}^3 z^5+22 \text{QuantumGroups$\grave{ }$a} z^5+26 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +7 \text{QuantumGroups$\grave{ }$a}^{10} z^4-9 \text{QuantumGroups$\grave{ }$a}^8 z^4-68 \text{QuantumGroups$\grave{ }$a}^6 z^4-129 \text{QuantumGroups$\grave{ }$a}^4 z^4-114 \text{QuantumGroups$\grave{ }$a}^2 z^4+4 z^4 $Failed^{-1} -33 z^4+\text{QuantumGroups$\grave{ }$a}^{11} z^3-9 \text{QuantumGroups$\grave{ }$a}^9 z^3-16 \text{QuantumGroups$\grave{ }$a}^7 z^3-15 \text{QuantumGroups$\grave{ }$a} z^3-9 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^{10} z^2+5 \text{QuantumGroups$\grave{ }$a}^8 z^2+22 \text{QuantumGroups$\grave{ }$a}^6 z^2+40 \text{QuantumGroups$\grave{ }$a}^4 z^2+34 \text{QuantumGroups$\grave{ }$a}^2 z^2+10 z^2+2 \text{QuantumGroups$\grave{ }$a}^9 z+\text{QuantumGroups$\grave{ }$a}^7 z-\text{QuantumGroups$\grave{ }$a}^5 z+\text{QuantumGroups$\grave{ }$a}^3 z+2 \text{QuantumGroups$\grave{ }$a} z+z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8-2 \text{QuantumGroups$\grave{ }$a}^6-3 \text{QuantumGroups$\grave{ }$a}^4-4 \text{QuantumGroups$\grave{ }$a}^2-1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
