K14a17877

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a17877

Polynomial invariants

Jones polynomial	Data:K14a17877/Jones Polynomial
Alexander polynomial	$3t^{4}-12t^{3}+29t^{2}-51t+63-51t^{-1}+29t^{-2}-12t^{-3}+3t^{-4}$
Conway polynomial	Data:K14a17877/Conway Polynomial
Determinant	Data:K14a17877/Determinant
Signature	Data:K14a17877/Signature
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}a^{-4}+z^{8}-a^{2}z^{6}+4z^{6}a^{-2}+5z^{6}a^{-4}-z^{6}a^{-6}+5z^{6}-4a^{2}z^{4}+6z^{4}a^{-2}+9z^{4}a^{-4}-4z^{4}a^{-6}+10z^{4}-6a^{2}z^{2}+3z^{2}a^{-2}+5z^{2}a^{-4}-5z^{2}a^{-6}+8z^{2}-2a^{2}+a^{-2}-a^{-6}+3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +5 z^{12} $Failed^{-1} +10 z^{12} $Failed^{-1} +5 z^{12} $Failed^{-1} +8 z^{11} $Failed^{-1} +2 z^{11} $Failed^{-1} -z^{11} $Failed^{-1} +5 z^{11} $Failed^{-1} -8 z^{10} $Failed^{-1} -47 z^{10} $Failed^{-1} -26 z^{10} $Failed^{-1} +3 z^{10} $Failed^{-1} +10 z^{10}+10 \text{QuantumGroups$\grave{ }$a} z^9-17 z^9 $Failed^{-1} -26 z^9 $Failed^{-1} -28 z^9 $Failed^{-1} -28 z^9 $Failed^{-1} +z^9 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^2 z^8-13 z^8 $Failed^{-1} +84 z^8 $Failed^{-1} +50 z^8 $Failed^{-1} -17 z^8 $Failed^{-1} -21 z^8+6 \text{QuantumGroups$\grave{ }$a}^3 z^7-16 \text{QuantumGroups$\grave{ }$a} z^7+6 z^7 $Failed^{-1} +36 z^7 $Failed^{-1} +68 z^7 $Failed^{-1} +54 z^7 $Failed^{-1} -6 z^7 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^4 z^6-15 \text{QuantumGroups$\grave{ }$a}^2 z^6+38 z^6 $Failed^{-1} -85 z^6 $Failed^{-1} -57 z^6 $Failed^{-1} +30 z^6 $Failed^{-1} +18 z^6+\text{QuantumGroups$\grave{ }$a}^5 z^5-8 \text{QuantumGroups$\grave{ }$a}^3 z^5+8 \text{QuantumGroups$\grave{ }$a} z^5+13 z^5 $Failed^{-1} -17 z^5 $Failed^{-1} -74 z^5 $Failed^{-1} -50 z^5 $Failed^{-1} +11 z^5 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^4 z^4+14 \text{QuantumGroups$\grave{ }$a}^2 z^4-36 z^4 $Failed^{-1} +45 z^4 $Failed^{-1} +40 z^4 $Failed^{-1} -18 z^4 $Failed^{-1} -5 z^4-2 \text{QuantumGroups$\grave{ }$a}^5 z^3+4 \text{QuantumGroups$\grave{ }$a}^3 z^3+3 \text{QuantumGroups$\grave{ }$a} z^3-14 z^3 $Failed^{-1} -z^3 $Failed^{-1} +42 z^3 $Failed^{-1} +26 z^3 $Failed^{-1} -6 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^2-8 \text{QuantumGroups$\grave{ }$a}^2 z^2+11 z^2 $Failed^{-1} -8 z^2 $Failed^{-1} -11 z^2 $Failed^{-1} +2 z^2 $Failed^{-1} -3 z^2+\text{QuantumGroups$\grave{ }$a}^5 z-\text{QuantumGroups$\grave{ }$a}^3 z-2 \text{QuantumGroups$\grave{ }$a} z+2 z $Failed^{-1} -8 z $Failed^{-1} -6 z $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} + $Failed^{-1} +3}

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