K14a1459

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a1459

Polynomial invariants

Jones polynomial	Data:K14a1459/Jones Polynomial
Alexander polynomial	$t^{5}-8t^{4}+26t^{3}-50t^{2}+69t-75+69t^{-1}-50t^{-2}+26t^{-3}-8t^{-4}+t^{-5}$
Conway polynomial	Data:K14a1459/Conway Polynomial
Determinant	Data:K14a1459/Determinant
Signature	Data:K14a1459/Signature
HOMFLY-PT polynomial	$z^{10}a^{-2}+6z^{8}a^{-2}-2z^{8}a^{-4}-2z^{8}+a^{2}z^{6}+15z^{6}a^{-2}-10z^{6}a^{-4}+z^{6}a^{-6}-10z^{6}+4a^{2}z^{4}+22z^{4}a^{-2}-17z^{4}a^{-4}+4z^{4}a^{-6}-17z^{4}+4a^{2}z^{2}+18z^{2}a^{-2}-13z^{2}a^{-4}+4z^{2}a^{-6}-13z^{2}+a^{2}+6a^{-2}-4a^{-4}+a^{-6}-3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +14 z^{12} $Failed^{-1} +7 z^{12} $Failed^{-1} +7 z^{12}+10 \text{QuantumGroups$\grave{ }$a} z^{11}+17 z^{11} $Failed^{-1} +18 z^{11} $Failed^{-1} +11 z^{11} $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-34 z^{10} $Failed^{-1} -3 z^{10} $Failed^{-1} +12 z^{10} $Failed^{-1} -11 z^{10}+4 \text{QuantumGroups$\grave{ }$a}^3 z^9-35 \text{QuantumGroups$\grave{ }$a} z^9-88 z^9 $Failed^{-1} -78 z^9 $Failed^{-1} -18 z^9 $Failed^{-1} +11 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^8-31 \text{QuantumGroups$\grave{ }$a}^2 z^8+z^8 $Failed^{-1} -24 z^8 $Failed^{-1} -17 z^8 $Failed^{-1} +8 z^8 $Failed^{-1} -32 z^8-16 \text{QuantumGroups$\grave{ }$a}^3 z^7+33 \text{QuantumGroups$\grave{ }$a} z^7+136 z^7 $Failed^{-1} +124 z^7 $Failed^{-1} +17 z^7 $Failed^{-1} -16 z^7 $Failed^{-1} +4 z^7 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^4 z^6+36 \text{QuantumGroups$\grave{ }$a}^2 z^6+67 z^6 $Failed^{-1} +51 z^6 $Failed^{-1} +7 z^6 $Failed^{-1} -14 z^6 $Failed^{-1} +z^6 $Failed^{-1} +78 z^6+18 \text{QuantumGroups$\grave{ }$a}^3 z^5-10 \text{QuantumGroups$\grave{ }$a} z^5-91 z^5 $Failed^{-1} -91 z^5 $Failed^{-1} -17 z^5 $Failed^{-1} +3 z^5 $Failed^{-1} -8 z^5 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^4 z^4-21 \text{QuantumGroups$\grave{ }$a}^2 z^4-71 z^4 $Failed^{-1} -45 z^4 $Failed^{-1} -4 z^4 $Failed^{-1} +7 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} -64 z^4-8 \text{QuantumGroups$\grave{ }$a}^3 z^3-2 \text{QuantumGroups$\grave{ }$a} z^3+26 z^3 $Failed^{-1} +31 z^3 $Failed^{-1} +10 z^3 $Failed^{-1} +4 z^3 $Failed^{-1} +5 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^4 z^2+7 \text{QuantumGroups$\grave{ }$a}^2 z^2+31 z^2 $Failed^{-1} +20 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} -z^2 $Failed^{-1} +z^2 $Failed^{-1} +24 z^2+\text{QuantumGroups$\grave{ }$a}^3 z+\text{QuantumGroups$\grave{ }$a} z-2 z $Failed^{-1} -3 z $Failed^{-1} -2 z $Failed^{-1} -2 z $Failed^{-1} -z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^2-6 $Failed^{-1} -4 $Failed^{-1} - $Failed^{-1} -3}

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