K14a6078

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a6078

Polynomial invariants

Jones polynomial	Data:K14a6078/Jones Polynomial
Alexander polynomial	$2t^{4}-13t^{3}+41t^{2}-80t+101-80t^{-1}+41t^{-2}-13t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a6078/Conway Polynomial
Determinant	Data:K14a6078/Determinant
Signature	Data:K14a6078/Signature
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}-a^{2}z^{6}+3z^{6}a^{-2}-3z^{6}a^{-4}+4z^{6}-3a^{2}z^{4}+5z^{4}a^{-2}-9z^{4}a^{-4}+3z^{4}a^{-6}+7z^{4}-3a^{2}z^{2}+4z^{2}a^{-2}-11z^{2}a^{-4}+6z^{2}a^{-6}-z^{2}a^{-8}+4z^{2}+2a^{-2}-5a^{-4}+4a^{-6}-a^{-8}+1$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +8 z^{12} $Failed^{-1} +14 z^{12} $Failed^{-1} +6 z^{12} $Failed^{-1} +15 z^{11} $Failed^{-1} +22 z^{11} $Failed^{-1} +14 z^{11} $Failed^{-1} +7 z^{11} $Failed^{-1} +3 z^{10} $Failed^{-1} -34 z^{10} $Failed^{-1} -14 z^{10} $Failed^{-1} +4 z^{10} $Failed^{-1} +19 z^{10}+19 \text{QuantumGroups$\grave{ }$a} z^9-23 z^9 $Failed^{-1} -97 z^9 $Failed^{-1} -87 z^9 $Failed^{-1} -31 z^9 $Failed^{-1} +z^9 $Failed^{-1} +15 \text{QuantumGroups$\grave{ }$a}^2 z^8-67 z^8 $Failed^{-1} -24 z^8 $Failed^{-1} -25 z^8 $Failed^{-1} -20 z^8 $Failed^{-1} -33 z^8+9 \text{QuantumGroups$\grave{ }$a}^3 z^7-32 \text{QuantumGroups$\grave{ }$a} z^7-7 z^7 $Failed^{-1} +123 z^7 $Failed^{-1} +135 z^7 $Failed^{-1} +41 z^7 $Failed^{-1} -5 z^7 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^4 z^6-22 \text{QuantumGroups$\grave{ }$a}^2 z^6+96 z^6 $Failed^{-1} +109 z^6 $Failed^{-1} +86 z^6 $Failed^{-1} +34 z^6 $Failed^{-1} +13 z^6+\text{QuantumGroups$\grave{ }$a}^5 z^5-10 \text{QuantumGroups$\grave{ }$a}^3 z^5+21 \text{QuantumGroups$\grave{ }$a} z^5+17 z^5 $Failed^{-1} -75 z^5 $Failed^{-1} -85 z^5 $Failed^{-1} -17 z^5 $Failed^{-1} +8 z^5 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^4 z^4+15 \text{QuantumGroups$\grave{ }$a}^2 z^4-63 z^4 $Failed^{-1} -98 z^4 $Failed^{-1} -77 z^4 $Failed^{-1} -26 z^4 $Failed^{-1} +3 z^4-\text{QuantumGroups$\grave{ }$a}^5 z^3+4 \text{QuantumGroups$\grave{ }$a}^3 z^3-6 \text{QuantumGroups$\grave{ }$a} z^3-7 z^3 $Failed^{-1} +28 z^3 $Failed^{-1} +29 z^3 $Failed^{-1} -5 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^2-4 \text{QuantumGroups$\grave{ }$a}^2 z^2+19 z^2 $Failed^{-1} +39 z^2 $Failed^{-1} +30 z^2 $Failed^{-1} +9 z^2 $Failed^{-1} -4 z^2+\text{QuantumGroups$\grave{ }$a} z-6 z $Failed^{-1} -6 z $Failed^{-1} +z $Failed^{-1} -2 $Failed^{-1} -5 $Failed^{-1} -4 $Failed^{-1} - $Failed^{-1} +1}

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