K14a17468

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a17468

Polynomial invariants

Jones polynomial	Data:K14a17468/Jones Polynomial
Alexander polynomial	$4t^{4}-14t^{3}+26t^{2}-38t+45-38t^{-1}+26t^{-2}-14t^{-3}+4t^{-4}$
Conway polynomial	Data:K14a17468/Conway Polynomial
Determinant	Data:K14a17468/Determinant
Signature	Data:K14a17468/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}a^{-2}+2z^{8}-a^{4}z^{6}+5a^{2}z^{6}+4z^{6}a^{-2}-z^{6}a^{-4}+11z^{6}-5a^{4}z^{4}+8a^{2}z^{4}+3z^{4}a^{-2}-4z^{4}a^{-4}+20z^{4}-7a^{4}z^{2}+5a^{2}z^{2}-3z^{2}a^{-2}-4z^{2}a^{-4}+13z^{2}-2a^{4}+2a^{2}-2a^{-2}+3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle \text{QuantumGroups$\grave{ }$a} z^{13}+z^{13} $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+3 z^{12} $Failed^{-1} +5 z^{12}+3 \text{QuantumGroups$\grave{ }$a}^3 z^{11}-\text{QuantumGroups$\grave{ }$a} z^{11}+z^{11} $Failed^{-1} +5 z^{11} $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-4 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-9 z^{10} $Failed^{-1} +6 z^{10} $Failed^{-1} -23 z^{10}+3 \text{QuantumGroups$\grave{ }$a}^5 z^9-9 \text{QuantumGroups$\grave{ }$a}^3 z^9+\text{QuantumGroups$\grave{ }$a} z^9-10 z^9 $Failed^{-1} -18 z^9 $Failed^{-1} +5 z^9 $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^6 z^8-18 \text{QuantumGroups$\grave{ }$a}^4 z^8-2 \text{QuantumGroups$\grave{ }$a}^2 z^8+15 z^8 $Failed^{-1} -23 z^8 $Failed^{-1} +3 z^8 $Failed^{-1} +59 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-11 \text{QuantumGroups$\grave{ }$a}^5 z^7+8 \text{QuantumGroups$\grave{ }$a}^3 z^7-5 \text{QuantumGroups$\grave{ }$a} z^7+23 z^7 $Failed^{-1} +29 z^7 $Failed^{-1} -18 z^7 $Failed^{-1} +z^7 $Failed^{-1} -8 \text{QuantumGroups$\grave{ }$a}^6 z^6+38 \text{QuantumGroups$\grave{ }$a}^4 z^6+22 \text{QuantumGroups$\grave{ }$a}^2 z^6-17 z^6 $Failed^{-1} +36 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} -88 z^6-5 \text{QuantumGroups$\grave{ }$a}^7 z^5+12 \text{QuantumGroups$\grave{ }$a}^5 z^5+8 \text{QuantumGroups$\grave{ }$a}^3 z^5+15 \text{QuantumGroups$\grave{ }$a} z^5-25 z^5 $Failed^{-1} -25 z^5 $Failed^{-1} +20 z^5 $Failed^{-1} -4 z^5 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^6 z^4-46 \text{QuantumGroups$\grave{ }$a}^4 z^4-30 \text{QuantumGroups$\grave{ }$a}^2 z^4+14 z^4 $Failed^{-1} -33 z^4 $Failed^{-1} +10 z^4 $Failed^{-1} +81 z^4+7 \text{QuantumGroups$\grave{ }$a}^7 z^3-6 \text{QuantumGroups$\grave{ }$a}^5 z^3-21 \text{QuantumGroups$\grave{ }$a}^3 z^3-4 \text{QuantumGroups$\grave{ }$a} z^3+22 z^3 $Failed^{-1} +3 z^3 $Failed^{-1} -11 z^3 $Failed^{-1} +4 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6 z^2+20 \text{QuantumGroups$\grave{ }$a}^4 z^2+13 \text{QuantumGroups$\grave{ }$a}^2 z^2-9 z^2 $Failed^{-1} +8 z^2 $Failed^{-1} -z^2 $Failed^{-1} -26 z^2-2 \text{QuantumGroups$\grave{ }$a}^7 z+\text{QuantumGroups$\grave{ }$a}^5 z+5 \text{QuantumGroups$\grave{ }$a}^3 z-\text{QuantumGroups$\grave{ }$a} z-5 z $Failed^{-1} +2 z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4-2 \text{QuantumGroups$\grave{ }$a}^2+2 $Failed^{-1} +3}

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