K14a13645

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13645

Polynomial invariants

Jones polynomial	Data:K14a13645/Jones Polynomial
Alexander polynomial	$-t^{5}+9t^{4}-41t^{3}+114t^{2}-207t+253-207t^{-1}+114t^{-2}-41t^{-3}+9t^{-4}-t^{-5}$
Conway polynomial	Data:K14a13645/Conway Polynomial
Determinant	Data:K14a13645/Determinant
Signature	Data:K14a13645/Signature
HOMFLY-PT polynomial	$-z^{10}+3a^{2}z^{8}+z^{8}a^{-2}-5z^{8}-3a^{4}z^{6}+9a^{2}z^{6}+3z^{6}a^{-2}-13z^{6}+a^{6}z^{4}-4a^{4}z^{4}+11a^{2}z^{4}+5z^{4}a^{-2}-15z^{4}-a^{4}z^{2}+5a^{2}z^{2}+3z^{2}a^{-2}-8z^{2}+a^{2}+a^{-2}-1$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 12 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+12 \text{QuantumGroups$\grave{ }$a} z^{13}+34 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+79 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+45 z^{12}+38 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+81 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+117 \text{QuantumGroups$\grave{ }$a} z^{11}+74 z^{11} $Failed^{-1} +22 \text{QuantumGroups$\grave{ }$a}^6 z^{10}-37 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-120 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+71 z^{10} $Failed^{-1} +10 z^{10}+7 \text{QuantumGroups$\grave{ }$a}^7 z^9-91 \text{QuantumGroups$\grave{ }$a}^5 z^9-288 \text{QuantumGroups$\grave{ }$a}^3 z^9-355 \text{QuantumGroups$\grave{ }$a} z^9-120 z^9 $Failed^{-1} +45 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^8-50 \text{QuantumGroups$\grave{ }$a}^6 z^8-70 \text{QuantumGroups$\grave{ }$a}^4 z^8-82 \text{QuantumGroups$\grave{ }$a}^2 z^8-124 z^8 $Failed^{-1} +20 z^8 $Failed^{-1} -207 z^8-12 \text{QuantumGroups$\grave{ }$a}^7 z^7+70 \text{QuantumGroups$\grave{ }$a}^5 z^7+274 \text{QuantumGroups$\grave{ }$a}^3 z^7+311 \text{QuantumGroups$\grave{ }$a} z^7+55 z^7 $Failed^{-1} -58 z^7 $Failed^{-1} +6 z^7 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8 z^6+37 \text{QuantumGroups$\grave{ }$a}^6 z^6+107 \text{QuantumGroups$\grave{ }$a}^4 z^6+181 \text{QuantumGroups$\grave{ }$a}^2 z^6+95 z^6 $Failed^{-1} -14 z^6 $Failed^{-1} +z^6 $Failed^{-1} +222 z^6+5 \text{QuantumGroups$\grave{ }$a}^7 z^5-18 \text{QuantumGroups$\grave{ }$a}^5 z^5-98 \text{QuantumGroups$\grave{ }$a}^3 z^5-124 \text{QuantumGroups$\grave{ }$a} z^5-14 z^5 $Failed^{-1} +34 z^5 $Failed^{-1} -z^5 $Failed^{-1} -9 \text{QuantumGroups$\grave{ }$a}^6 z^4-36 \text{QuantumGroups$\grave{ }$a}^4 z^4-80 \text{QuantumGroups$\grave{ }$a}^2 z^4-41 z^4 $Failed^{-1} +5 z^4 $Failed^{-1} -99 z^4+2 \text{QuantumGroups$\grave{ }$a}^5 z^3+18 \text{QuantumGroups$\grave{ }$a}^3 z^3+29 \text{QuantumGroups$\grave{ }$a} z^3+6 z^3 $Failed^{-1} -7 z^3 $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^4 z^2+13 \text{QuantumGroups$\grave{ }$a}^2 z^2+9 z^2 $Failed^{-1} +20 z^2-\text{QuantumGroups$\grave{ }$a}^5 z-3 \text{QuantumGroups$\grave{ }$a}^3 z-4 \text{QuantumGroups$\grave{ }$a} z-2 z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} -1}

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