K14a3066

Knot presentations

Dowker-Thistlethwaite code

4 10 12 18 16 2 20 24 8 6 28 26 14 22

Notes on presentations of K14a3066

Polynomial invariants

Jones polynomial	Data:K14a3066/Jones Polynomial
Alexander polynomial	$-4t^{3}+26t^{2}-69t+95-69t^{-1}+26t^{-2}-4t^{-3}$
Conway polynomial	Data:K14a3066/Conway Polynomial
Determinant	Data:K14a3066/Determinant
Signature	Data:K14a3066/Signature
HOMFLY-PT polynomial	$a^{8}-3z^{2}a^{6}-2a^{6}+3z^{4}a^{4}+2z^{2}a^{4}-z^{6}a^{2}+2z^{4}a^{2}+4z^{2}a^{2}+3a^{2}-2z^{6}-3z^{4}-4z^{2}-2-z^{6}a^{-2}-z^{4}a^{-2}-z^{2}a^{-2}+a^{-2}+z^{4}a^{-4}+z^{2}a^{-4}$
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{QuantumGroups$\grave{ }$a}^3 z^{13}+\text{QuantumGroups$\grave{ }$a} z^{13}+3 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+8 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+5 z^{12}+4 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+8 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+14 \text{QuantumGroups$\grave{ }$a} z^{11}+10 z^{11} $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^{10}-4 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-24 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+12 z^{10} $Failed^{-1} -4 z^{10}+3 \text{QuantumGroups$\grave{ }$a}^7 z^9-9 \text{QuantumGroups$\grave{ }$a}^5 z^9-42 \text{QuantumGroups$\grave{ }$a}^3 z^9-70 \text{QuantumGroups$\grave{ }$a} z^9-29 z^9 $Failed^{-1} +11 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^8-13 \text{QuantumGroups$\grave{ }$a}^6 z^8-7 \text{QuantumGroups$\grave{ }$a}^4 z^8+23 \text{QuantumGroups$\grave{ }$a}^2 z^8-33 z^8 $Failed^{-1} +8 z^8 $Failed^{-1} -25 z^8-14 \text{QuantumGroups$\grave{ }$a}^7 z^7-7 \text{QuantumGroups$\grave{ }$a}^5 z^7+79 \text{QuantumGroups$\grave{ }$a}^3 z^7+142 \text{QuantumGroups$\grave{ }$a} z^7+39 z^7 $Failed^{-1} -27 z^7 $Failed^{-1} +4 z^7 $Failed^{-1} -5 \text{QuantumGroups$\grave{ }$a}^8 z^6+4 \text{QuantumGroups$\grave{ }$a}^6 z^6+3 \text{QuantumGroups$\grave{ }$a}^4 z^6+11 \text{QuantumGroups$\grave{ }$a}^2 z^6+36 z^6 $Failed^{-1} -19 z^6 $Failed^{-1} +z^6 $Failed^{-1} +73 z^6+21 \text{QuantumGroups$\grave{ }$a}^7 z^5+21 \text{QuantumGroups$\grave{ }$a}^5 z^5-82 \text{QuantumGroups$\grave{ }$a}^3 z^5-131 \text{QuantumGroups$\grave{ }$a} z^5-20 z^5 $Failed^{-1} +20 z^5 $Failed^{-1} -9 z^5 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^8 z^4+15 \text{QuantumGroups$\grave{ }$a}^6 z^4+7 \text{QuantumGroups$\grave{ }$a}^4 z^4-37 \text{QuantumGroups$\grave{ }$a}^2 z^4-13 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} -63 z^4-13 \text{QuantumGroups$\grave{ }$a}^7 z^3-12 \text{QuantumGroups$\grave{ }$a}^5 z^3+38 \text{QuantumGroups$\grave{ }$a}^3 z^3+51 \text{QuantumGroups$\grave{ }$a} z^3+8 z^3 $Failed^{-1} -3 z^3 $Failed^{-1} +3 z^3 $Failed^{-1} -5 \text{QuantumGroups$\grave{ }$a}^8 z^2-12 \text{QuantumGroups$\grave{ }$a}^6 z^2-3 \text{QuantumGroups$\grave{ }$a}^4 z^2+19 \text{QuantumGroups$\grave{ }$a}^2 z^2+3 z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +20 z^2+3 \text{QuantumGroups$\grave{ }$a}^7 z+3 \text{QuantumGroups$\grave{ }$a}^5 z-5 \text{QuantumGroups$\grave{ }$a}^3 z-8 \text{QuantumGroups$\grave{ }$a} z-3 z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8+2 \text{QuantumGroups$\grave{ }$a}^6-3 \text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} -2}

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Large Knot Page master template. Back to the top.