K14a87

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a87

Polynomial invariants

Jones polynomial	Data:K14a87/Jones Polynomial
Alexander polynomial	$-t^{5}+7t^{4}-26t^{3}+65t^{2}-112t+135-112t^{-1}+65t^{-2}-26t^{-3}+7t^{-4}-t^{-5}$
Conway polynomial	Data:K14a87/Conway Polynomial
Determinant	Data:K14a87/Determinant
Signature	Data:K14a87/Signature
HOMFLY-PT polynomial	$-z^{10}+2a^{2}z^{8}+2z^{8}a^{-2}-7z^{8}-a^{4}z^{6}+11a^{2}z^{6}+10z^{6}a^{-2}-z^{6}a^{-4}-24z^{6}-4a^{4}z^{4}+27a^{2}z^{4}+22z^{4}a^{-2}-3z^{4}a^{-4}-43z^{4}-7a^{4}z^{2}+30a^{2}z^{2}+22z^{2}a^{-2}-4z^{2}a^{-4}-40z^{2}-4a^{4}+13a^{2}+9a^{-2}-2a^{-4}-15$
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} z^{13}+z^{13} $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+6 z^{12} $Failed^{-1} +12 z^{12}+13 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+37 \text{QuantumGroups$\grave{ }$a} z^{11}+38 z^{11} $Failed^{-1} +14 z^{11} $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+34 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+42 z^{10} $Failed^{-1} +17 z^{10} $Failed^{-1} +45 z^{10}+9 \text{QuantumGroups$\grave{ }$a}^5 z^9-9 \text{QuantumGroups$\grave{ }$a}^3 z^9-68 \text{QuantumGroups$\grave{ }$a} z^9-60 z^9 $Failed^{-1} +2 z^9 $Failed^{-1} +12 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^8-30 \text{QuantumGroups$\grave{ }$a}^4 z^8-129 \text{QuantumGroups$\grave{ }$a}^2 z^8-142 z^8 $Failed^{-1} -31 z^8 $Failed^{-1} +5 z^8 $Failed^{-1} -201 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-20 \text{QuantumGroups$\grave{ }$a}^5 z^7-27 \text{QuantumGroups$\grave{ }$a}^3 z^7+3 \text{QuantumGroups$\grave{ }$a} z^7-31 z^7 $Failed^{-1} -68 z^7 $Failed^{-1} -27 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+32 \text{QuantumGroups$\grave{ }$a}^4 z^6+186 \text{QuantumGroups$\grave{ }$a}^2 z^6+164 z^6 $Failed^{-1} +16 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +281 z^6-3 \text{QuantumGroups$\grave{ }$a}^7 z^5+16 \text{QuantumGroups$\grave{ }$a}^5 z^5+50 \text{QuantumGroups$\grave{ }$a}^3 z^5+77 \text{QuantumGroups$\grave{ }$a} z^5+110 z^5 $Failed^{-1} +89 z^5 $Failed^{-1} +23 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^6 z^4-29 \text{QuantumGroups$\grave{ }$a}^4 z^4-149 \text{QuantumGroups$\grave{ }$a}^2 z^4-104 z^4 $Failed^{-1} -5 z^4 $Failed^{-1} +8 z^4 $Failed^{-1} -203 z^4+3 \text{QuantumGroups$\grave{ }$a}^7 z^3-7 \text{QuantumGroups$\grave{ }$a}^5 z^3-37 \text{QuantumGroups$\grave{ }$a}^3 z^3-65 \text{QuantumGroups$\grave{ }$a} z^3-75 z^3 $Failed^{-1} -49 z^3 $Failed^{-1} -11 z^3 $Failed^{-1} +z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6 z^2+17 \text{QuantumGroups$\grave{ }$a}^4 z^2+66 \text{QuantumGroups$\grave{ }$a}^2 z^2+42 z^2 $Failed^{-1} +4 z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +83 z^2-\text{QuantumGroups$\grave{ }$a}^7 z+2 \text{QuantumGroups$\grave{ }$a}^5 z+10 \text{QuantumGroups$\grave{ }$a}^3 z+16 \text{QuantumGroups$\grave{ }$a} z+17 z $Failed^{-1} +11 z $Failed^{-1} +3 z $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^4-13 \text{QuantumGroups$\grave{ }$a}^2-9 $Failed^{-1} -2 $Failed^{-1} -15}

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