K14a2526

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a2526

Polynomial invariants

Jones polynomial	Data:K14a2526/Jones Polynomial
Alexander polynomial	$-3t^{4}+20t^{3}-57t^{2}+94t-107+94t^{-1}-57t^{-2}+20t^{-3}-3t^{-4}$
Conway polynomial	Data:K14a2526/Conway Polynomial
Determinant	Data:K14a2526/Determinant
Signature	Data:K14a2526/Signature
HOMFLY-PT polynomial	$-a^{2}z^{8}-2z^{8}+2a^{4}z^{6}-a^{2}z^{6}+3z^{6}a^{-2}-8z^{6}-a^{6}z^{4}+5a^{4}z^{4}+4a^{2}z^{4}+9z^{4}a^{-2}-z^{4}a^{-4}-13z^{4}-2a^{6}z^{2}+2a^{4}z^{2}+5a^{2}z^{2}+7z^{2}a^{-2}-2z^{2}a^{-4}-12z^{2}+2a^{2}+2a^{-2}-3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a} z^{13}+2 z^{13} $Failed^{-1} +10 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+7 z^{12} $Failed^{-1} +17 z^{12}+21 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+38 \text{QuantumGroups$\grave{ }$a} z^{11}+26 z^{11} $Failed^{-1} +9 z^{11} $Failed^{-1} +26 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+20 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-5 z^{10} $Failed^{-1} +5 z^{10} $Failed^{-1} -16 z^{10}+23 \text{QuantumGroups$\grave{ }$a}^5 z^9-30 \text{QuantumGroups$\grave{ }$a}^3 z^9-136 \text{QuantumGroups$\grave{ }$a} z^9-118 z^9 $Failed^{-1} -34 z^9 $Failed^{-1} +z^9 $Failed^{-1} +16 \text{QuantumGroups$\grave{ }$a}^6 z^8-53 \text{QuantumGroups$\grave{ }$a}^4 z^8-145 \text{QuantumGroups$\grave{ }$a}^2 z^8-67 z^8 $Failed^{-1} -22 z^8 $Failed^{-1} -121 z^8+9 \text{QuantumGroups$\grave{ }$a}^7 z^7-42 \text{QuantumGroups$\grave{ }$a}^5 z^7-30 \text{QuantumGroups$\grave{ }$a}^3 z^7+114 \text{QuantumGroups$\grave{ }$a} z^7+133 z^7 $Failed^{-1} +36 z^7 $Failed^{-1} -4 z^7 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^8 z^6-22 \text{QuantumGroups$\grave{ }$a}^6 z^6+36 \text{QuantumGroups$\grave{ }$a}^4 z^6+192 \text{QuantumGroups$\grave{ }$a}^2 z^6+139 z^6 $Failed^{-1} +35 z^6 $Failed^{-1} +234 z^6+\text{QuantumGroups$\grave{ }$a}^9 z^5-9 \text{QuantumGroups$\grave{ }$a}^7 z^5+33 \text{QuantumGroups$\grave{ }$a}^5 z^5+64 \text{QuantumGroups$\grave{ }$a}^3 z^5-2 \text{QuantumGroups$\grave{ }$a} z^5-31 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +6 z^5 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^8 z^4+13 \text{QuantumGroups$\grave{ }$a}^6 z^4-11 \text{QuantumGroups$\grave{ }$a}^4 z^4-106 \text{QuantumGroups$\grave{ }$a}^2 z^4-96 z^4 $Failed^{-1} -24 z^4 $Failed^{-1} -150 z^4-\text{QuantumGroups$\grave{ }$a}^9 z^3+3 \text{QuantumGroups$\grave{ }$a}^7 z^3-13 \text{QuantumGroups$\grave{ }$a}^5 z^3-37 \text{QuantumGroups$\grave{ }$a}^3 z^3-27 \text{QuantumGroups$\grave{ }$a} z^3-16 z^3 $Failed^{-1} -13 z^3 $Failed^{-1} -4 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^2-2 \text{QuantumGroups$\grave{ }$a}^6 z^2+\text{QuantumGroups$\grave{ }$a}^4 z^2+25 \text{QuantumGroups$\grave{ }$a}^2 z^2+25 z^2 $Failed^{-1} +6 z^2 $Failed^{-1} +40 z^2+2 \text{QuantumGroups$\grave{ }$a}^5 z+7 \text{QuantumGroups$\grave{ }$a}^3 z+8 \text{QuantumGroups$\grave{ }$a} z+6 z $Failed^{-1} +4 z $Failed^{-1} +z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^2-2 $Failed^{-1} -3}

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