K14a3057

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a3057

Polynomial invariants

Jones polynomial	Data:K14a3057/Jones Polynomial
Alexander polynomial	$2t^{4}-15t^{3}+53t^{2}-107t+135-107t^{-1}+53t^{-2}-15t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a3057/Conway Polynomial
Determinant	Data:K14a3057/Determinant
Signature	Data:K14a3057/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}-2a^{4}z^{6}+3a^{2}z^{6}-2z^{6}a^{-2}+2z^{6}+a^{6}z^{4}-6a^{4}z^{4}+7a^{2}z^{4}-3z^{4}a^{-2}+z^{4}a^{-4}+3z^{4}+2a^{6}z^{2}-8a^{4}z^{2}+8a^{2}z^{2}-2z^{2}a^{-2}+2z^{2}+a^{6}-4a^{4}+4a^{2}-a^{-2}+1$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle \text{QuantumGroups$\grave{ }$a}^3 z^{13}+\text{QuantumGroups$\grave{ }$a} z^{13}+4 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+10 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+6 z^{12}+7 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+21 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+30 \text{QuantumGroups$\grave{ }$a} z^{11}+16 z^{11} $Failed^{-1} +7 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+13 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+18 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+25 z^{10} $Failed^{-1} +37 z^{10}+4 \text{QuantumGroups$\grave{ }$a}^7 z^9-10 \text{QuantumGroups$\grave{ }$a}^5 z^9-48 \text{QuantumGroups$\grave{ }$a}^3 z^9-50 \text{QuantumGroups$\grave{ }$a} z^9+9 z^9 $Failed^{-1} +25 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^8-23 \text{QuantumGroups$\grave{ }$a}^6 z^8-71 \text{QuantumGroups$\grave{ }$a}^4 z^8-110 \text{QuantumGroups$\grave{ }$a}^2 z^8-29 z^8 $Failed^{-1} +16 z^8 $Failed^{-1} -108 z^8-16 \text{QuantumGroups$\grave{ }$a}^7 z^7-23 \text{QuantumGroups$\grave{ }$a}^5 z^7+4 \text{QuantumGroups$\grave{ }$a}^3 z^7-17 \text{QuantumGroups$\grave{ }$a} z^7-73 z^7 $Failed^{-1} -39 z^7 $Failed^{-1} +6 z^7 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^8 z^6+23 \text{QuantumGroups$\grave{ }$a}^6 z^6+96 \text{QuantumGroups$\grave{ }$a}^4 z^6+143 \text{QuantumGroups$\grave{ }$a}^2 z^6-8 z^6 $Failed^{-1} -22 z^6 $Failed^{-1} +z^6 $Failed^{-1} +89 z^6+22 \text{QuantumGroups$\grave{ }$a}^7 z^5+54 \text{QuantumGroups$\grave{ }$a}^5 z^5+59 \text{QuantumGroups$\grave{ }$a}^3 z^5+71 \text{QuantumGroups$\grave{ }$a} z^5+63 z^5 $Failed^{-1} +14 z^5 $Failed^{-1} -5 z^5 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^8 z^4-8 \text{QuantumGroups$\grave{ }$a}^6 z^4-58 \text{QuantumGroups$\grave{ }$a}^4 z^4-78 \text{QuantumGroups$\grave{ }$a}^2 z^4+14 z^4 $Failed^{-1} +6 z^4 $Failed^{-1} -25 z^4-13 \text{QuantumGroups$\grave{ }$a}^7 z^3-39 \text{QuantumGroups$\grave{ }$a}^5 z^3-52 \text{QuantumGroups$\grave{ }$a}^3 z^3-42 \text{QuantumGroups$\grave{ }$a} z^3-15 z^3 $Failed^{-1} +z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^8 z^2+2 \text{QuantumGroups$\grave{ }$a}^6 z^2+19 \text{QuantumGroups$\grave{ }$a}^4 z^2+20 \text{QuantumGroups$\grave{ }$a}^2 z^2-4 z^2 $Failed^{-1} +z^2+3 \text{QuantumGroups$\grave{ }$a}^7 z+11 \text{QuantumGroups$\grave{ }$a}^5 z+14 \text{QuantumGroups$\grave{ }$a}^3 z+8 \text{QuantumGroups$\grave{ }$a} z+z $Failed^{-1} -z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6-4 \text{QuantumGroups$\grave{ }$a}^4-4 \text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} +1}

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