K14n18209

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14n18209

Polynomial invariants

Jones polynomial	Data:K14n18209/Jones Polynomial
Alexander polynomial	[math]\displaystyle{ t^4-4 t^3+11 t^2-22 t+29-22 t^{-1} +11 t^{-2} -4 t^{-3} + t^{-4} }[/math]
Conway polynomial	Data:K14n18209/Conway Polynomial
Determinant	Data:K14n18209/Determinant
Signature	Data:K14n18209/Signature
HOMFLY-PT polynomial	[math]\displaystyle{ z^8 a^{-2} +a^2 z^6+5 z^6 a^{-2} -z^6 a^{-4} -z^6-a^4 z^4+5 a^2 z^4+9 z^4 a^{-2} -3 z^4 a^{-4} -3 z^4-3 a^4 z^2+7 a^2 z^2+5 z^2 a^{-2} -3 z^2 a^{-4} -4 z^2-2 a^4+4 a^2-1 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{12} $Failed^{-1} +z^{12}+\text{QuantumGroups$\grave{ }$a}^3 z^{11}+2 \text{QuantumGroups$\grave{ }$a} z^{11}+5 z^{11} $Failed^{-1} +4 z^{11} $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+3 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+4 z^{10} $Failed^{-1} +7 z^{10} $Failed^{-1} -2 z^{10}+\text{QuantumGroups$\grave{ }$a}^5 z^9-5 \text{QuantumGroups$\grave{ }$a}^3 z^9-14 \text{QuantumGroups$\grave{ }$a} z^9-24 z^9 $Failed^{-1} -9 z^9 $Failed^{-1} +7 z^9 $Failed^{-1} -14 \text{QuantumGroups$\grave{ }$a}^4 z^8-27 \text{QuantumGroups$\grave{ }$a}^2 z^8-30 z^8 $Failed^{-1} -22 z^8 $Failed^{-1} +4 z^8 $Failed^{-1} -17 z^8-7 \text{QuantumGroups$\grave{ }$a}^5 z^7-4 \text{QuantumGroups$\grave{ }$a}^3 z^7+16 \text{QuantumGroups$\grave{ }$a} z^7+32 z^7 $Failed^{-1} -5 z^7 $Failed^{-1} -23 z^7 $Failed^{-1} +z^7 $Failed^{-1} +30 \text{QuantumGroups$\grave{ }$a}^4 z^6+61 \text{QuantumGroups$\grave{ }$a}^2 z^6+46 z^6 $Failed^{-1} +15 z^6 $Failed^{-1} -13 z^6 $Failed^{-1} +49 z^6+16 \text{QuantumGroups$\grave{ }$a}^5 z^5+32 \text{QuantumGroups$\grave{ }$a}^3 z^5+21 \text{QuantumGroups$\grave{ }$a} z^5-4 z^5 $Failed^{-1} +12 z^5 $Failed^{-1} +18 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} -27 \text{QuantumGroups$\grave{ }$a}^4 z^4-48 \text{QuantumGroups$\grave{ }$a}^2 z^4-26 z^4 $Failed^{-1} -7 z^4 $Failed^{-1} +10 z^4 $Failed^{-1} -30 z^4-15 \text{QuantumGroups$\grave{ }$a}^5 z^3-35 \text{QuantumGroups$\grave{ }$a}^3 z^3-30 \text{QuantumGroups$\grave{ }$a} z^3-10 z^3 $Failed^{-1} -9 z^3 $Failed^{-1} -7 z^3 $Failed^{-1} +2 z^3 $Failed^{-1} +11 \text{QuantumGroups$\grave{ }$a}^4 z^2+16 \text{QuantumGroups$\grave{ }$a}^2 z^2+4 z^2 $Failed^{-1} +z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +6 z^2+5 \text{QuantumGroups$\grave{ }$a}^5 z+11 \text{QuantumGroups$\grave{ }$a}^3 z+10 \text{QuantumGroups$\grave{ }$a} z+6 z $Failed^{-1} +3 z $Failed^{-1} +z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4-4 \text{QuantumGroups$\grave{ }$a}^2-1 }[/math]

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