K14a18143

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18143

Polynomial invariants

Jones polynomial	Data:K14a18143/Jones Polynomial
Alexander polynomial	$t^{5}-9t^{4}+36t^{3}-84t^{2}+131t-149+131t^{-1}-84t^{-2}+36t^{-3}-9t^{-4}+t^{-5}$
Conway polynomial	Data:K14a18143/Conway Polynomial
Determinant	Data:K14a18143/Determinant
Signature	Data:K14a18143/Signature
HOMFLY-PT polynomial	$z^{10}a^{-2}+5z^{8}a^{-2}-2z^{8}a^{-4}-2z^{8}+a^{2}z^{6}+11z^{6}a^{-2}-7z^{6}a^{-4}+z^{6}a^{-6}-7z^{6}+2a^{2}z^{4}+12z^{4}a^{-2}-7z^{4}a^{-4}+2z^{4}a^{-6}-7z^{4}+4z^{2}a^{-2}-2z^{2}a^{-4}-2z^{2}+1$
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 7 z^{13} $Failed^{-1} +7 z^{13} $Failed^{-1} +42 z^{12} $Failed^{-1} +22 z^{12} $Failed^{-1} +20 z^{12}+24 \text{QuantumGroups$\grave{ }$a} z^{11}+33 z^{11} $Failed^{-1} +43 z^{11} $Failed^{-1} +34 z^{11} $Failed^{-1} +16 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-103 z^{10} $Failed^{-1} -9 z^{10} $Failed^{-1} +37 z^{10} $Failed^{-1} -41 z^{10}+6 \text{QuantumGroups$\grave{ }$a}^3 z^9-76 \text{QuantumGroups$\grave{ }$a} z^9-165 z^9 $Failed^{-1} -159 z^9 $Failed^{-1} -46 z^9 $Failed^{-1} +30 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^8-50 \text{QuantumGroups$\grave{ }$a}^2 z^8+49 z^8 $Failed^{-1} -61 z^8 $Failed^{-1} -56 z^8 $Failed^{-1} +17 z^8 $Failed^{-1} -14 z^8-16 \text{QuantumGroups$\grave{ }$a}^3 z^7+72 \text{QuantumGroups$\grave{ }$a} z^7+210 z^7 $Failed^{-1} +168 z^7 $Failed^{-1} -4 z^7 $Failed^{-1} -44 z^7 $Failed^{-1} +6 z^7 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4 z^6+43 \text{QuantumGroups$\grave{ }$a}^2 z^6+53 z^6 $Failed^{-1} +68 z^6 $Failed^{-1} +15 z^6 $Failed^{-1} -20 z^6 $Failed^{-1} +z^6 $Failed^{-1} +66 z^6+8 \text{QuantumGroups$\grave{ }$a}^3 z^5-25 \text{QuantumGroups$\grave{ }$a} z^5-91 z^5 $Failed^{-1} -57 z^5 $Failed^{-1} +21 z^5 $Failed^{-1} +16 z^5 $Failed^{-1} -4 z^5 $Failed^{-1} -12 \text{QuantumGroups$\grave{ }$a}^2 z^4-48 z^4 $Failed^{-1} -23 z^4 $Failed^{-1} +5 z^4 $Failed^{-1} +5 z^4 $Failed^{-1} -37 z^4+2 \text{QuantumGroups$\grave{ }$a} z^3+4 z^3 $Failed^{-1} -4 z^3 $Failed^{-1} -7 z^3 $Failed^{-1} -z^3 $Failed^{-1} +9 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} -z^2 $Failed^{-1} +5 z^2+\text{QuantumGroups$\grave{ }$a} z+3 z $Failed^{-1} +3 z $Failed^{-1} +z $Failed^{-1} +1}

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