K14a18187

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18187

Polynomial invariants

Jones polynomial	Data:K14a18187/Jones Polynomial
Alexander polynomial	$4t^{4}-28t^{3}+85t^{2}-154t+187-154t^{-1}+85t^{-2}-28t^{-3}+4t^{-4}$
Conway polynomial	Data:K14a18187/Conway Polynomial
Determinant	Data:K14a18187/Determinant
Signature	Data:K14a18187/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}a^{-2}+2z^{8}-a^{4}z^{6}+a^{2}z^{6}+z^{6}a^{-2}-z^{6}a^{-4}+4z^{6}-a^{4}z^{4}-a^{2}z^{4}-z^{4}a^{-2}-z^{4}a^{-4}+z^{4}+a^{4}z^{2}-2a^{2}z^{2}-2z^{2}a^{-2}+z^{2}a^{-4}+a^{4}-2a^{2}-2a^{-2}+a^{-4}+3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 8 \text{QuantumGroups$\grave{ }$a} z^{13}+8 z^{13} $Failed^{-1} +24 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+24 z^{12} $Failed^{-1} +48 z^{12}+32 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+44 \text{QuantumGroups$\grave{ }$a} z^{11}+44 z^{11} $Failed^{-1} +32 z^{11} $Failed^{-1} +27 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-29 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-29 z^{10} $Failed^{-1} +27 z^{10} $Failed^{-1} -112 z^{10}+16 \text{QuantumGroups$\grave{ }$a}^5 z^9-68 \text{QuantumGroups$\grave{ }$a}^3 z^9-172 \text{QuantumGroups$\grave{ }$a} z^9-172 z^9 $Failed^{-1} -68 z^9 $Failed^{-1} +16 z^9 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^6 z^8-56 \text{QuantumGroups$\grave{ }$a}^4 z^8-23 \text{QuantumGroups$\grave{ }$a}^2 z^8-23 z^8 $Failed^{-1} -56 z^8 $Failed^{-1} +6 z^8 $Failed^{-1} +78 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-31 \text{QuantumGroups$\grave{ }$a}^5 z^7+48 \text{QuantumGroups$\grave{ }$a}^3 z^7+214 \text{QuantumGroups$\grave{ }$a} z^7+214 z^7 $Failed^{-1} +48 z^7 $Failed^{-1} -31 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+32 \text{QuantumGroups$\grave{ }$a}^4 z^6+48 \text{QuantumGroups$\grave{ }$a}^2 z^6+48 z^6 $Failed^{-1} +32 z^6 $Failed^{-1} -10 z^6 $Failed^{-1} +12 z^6-\text{QuantumGroups$\grave{ }$a}^7 z^5+14 \text{QuantumGroups$\grave{ }$a}^5 z^5-17 \text{QuantumGroups$\grave{ }$a}^3 z^5-104 \text{QuantumGroups$\grave{ }$a} z^5-104 z^5 $Failed^{-1} -17 z^5 $Failed^{-1} +14 z^5 $Failed^{-1} -z^5 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^6 z^4-6 \text{QuantumGroups$\grave{ }$a}^4 z^4-19 \text{QuantumGroups$\grave{ }$a}^2 z^4-19 z^4 $Failed^{-1} -6 z^4 $Failed^{-1} +3 z^4 $Failed^{-1} -20 z^4+\text{QuantumGroups$\grave{ }$a}^3 z^3+15 \text{QuantumGroups$\grave{ }$a} z^3+15 z^3 $Failed^{-1} +z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^2-2 \text{QuantumGroups$\grave{ }$a}^4 z^2-2 \text{QuantumGroups$\grave{ }$a}^2 z^2-2 z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +z^2 $Failed^{-1} +2 z^2-\text{QuantumGroups$\grave{ }$a}^5 z-\text{QuantumGroups$\grave{ }$a}^3 z-z $Failed^{-1} -z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4+2 \text{QuantumGroups$\grave{ }$a}^2+2 $Failed^{-1} + $Failed^{-1} +3}

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