K14a18410

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18410

Polynomial invariants

Jones polynomial	Data:K14a18410/Jones Polynomial
Alexander polynomial	$4t^{4}-16t^{3}+37t^{2}-62t+75-62t^{-1}+37t^{-2}-16t^{-3}+4t^{-4}$
Conway polynomial	Data:K14a18410/Conway Polynomial
Determinant	Data:K14a18410/Determinant
Signature	Data:K14a18410/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}a^{-2}+2z^{8}-a^{4}z^{6}+4a^{2}z^{6}+4z^{6}a^{-2}-z^{6}a^{-4}+10z^{6}-4a^{4}z^{4}+5a^{2}z^{4}+5z^{4}a^{-2}-4z^{4}a^{-4}+19z^{4}-5a^{4}z^{2}-5z^{2}a^{-4}+16z^{2}-a^{4}-2a^{2}-2a^{-2}-a^{-4}+7$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle \text{QuantumGroups$\grave{ }$a} z^{13}+z^{13} $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+4 z^{12} $Failed^{-1} +8 z^{12}+7 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+11 \text{QuantumGroups$\grave{ }$a} z^{11}+11 z^{11} $Failed^{-1} +7 z^{11} $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-3 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-3 z^{10} $Failed^{-1} +8 z^{10} $Failed^{-1} -22 z^{10}+6 \text{QuantumGroups$\grave{ }$a}^5 z^9-19 \text{QuantumGroups$\grave{ }$a}^3 z^9-45 \text{QuantumGroups$\grave{ }$a} z^9-45 z^9 $Failed^{-1} -19 z^9 $Failed^{-1} +6 z^9 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^6 z^8-28 \text{QuantumGroups$\grave{ }$a}^4 z^8-9 \text{QuantumGroups$\grave{ }$a}^2 z^8-9 z^8 $Failed^{-1} -28 z^8 $Failed^{-1} +3 z^8 $Failed^{-1} +44 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-21 \text{QuantumGroups$\grave{ }$a}^5 z^7+22 \text{QuantumGroups$\grave{ }$a}^3 z^7+88 \text{QuantumGroups$\grave{ }$a} z^7+88 z^7 $Failed^{-1} +22 z^7 $Failed^{-1} -21 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+44 \text{QuantumGroups$\grave{ }$a}^4 z^6+17 \text{QuantumGroups$\grave{ }$a}^2 z^6+17 z^6 $Failed^{-1} +44 z^6 $Failed^{-1} -10 z^6 $Failed^{-1} -74 z^6-4 \text{QuantumGroups$\grave{ }$a}^7 z^5+27 \text{QuantumGroups$\grave{ }$a}^5 z^5-9 \text{QuantumGroups$\grave{ }$a}^3 z^5-99 \text{QuantumGroups$\grave{ }$a} z^5-99 z^5 $Failed^{-1} -9 z^5 $Failed^{-1} +27 z^5 $Failed^{-1} -4 z^5 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^6 z^4-40 \text{QuantumGroups$\grave{ }$a}^4 z^4-5 \text{QuantumGroups$\grave{ }$a}^2 z^4-5 z^4 $Failed^{-1} -40 z^4 $Failed^{-1} +8 z^4 $Failed^{-1} +86 z^4+4 \text{QuantumGroups$\grave{ }$a}^7 z^3-19 \text{QuantumGroups$\grave{ }$a}^5 z^3-9 \text{QuantumGroups$\grave{ }$a}^3 z^3+68 \text{QuantumGroups$\grave{ }$a} z^3+68 z^3 $Failed^{-1} -9 z^3 $Failed^{-1} -19 z^3 $Failed^{-1} +4 z^3 $Failed^{-1} +11 \text{QuantumGroups$\grave{ }$a}^4 z^2-7 \text{QuantumGroups$\grave{ }$a}^2 z^2-7 z^2 $Failed^{-1} +11 z^2 $Failed^{-1} -36 z^2+5 \text{QuantumGroups$\grave{ }$a}^5 z+\text{QuantumGroups$\grave{ }$a}^3 z-16 \text{QuantumGroups$\grave{ }$a} z-16 z $Failed^{-1} +z $Failed^{-1} +5 z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^4+2 \text{QuantumGroups$\grave{ }$a}^2+2 $Failed^{-1} - $Failed^{-1} +7}

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