K14a18082

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18082

Polynomial invariants

Jones polynomial	Data:K14a18082/Jones Polynomial
Alexander polynomial	$2t^{5}-10t^{4}+29t^{3}-60t^{2}+93t-107+93t^{-1}-60t^{-2}+29t^{-3}-10t^{-4}+2t^{-5}$
Conway polynomial	Data:K14a18082/Conway Polynomial
Determinant	Data:K14a18082/Determinant
Signature	Data:K14a18082/Signature
HOMFLY-PT polynomial	$a^{4}z^{10}+a^{2}z^{10}-a^{6}z^{8}+6a^{4}z^{8}+6a^{2}z^{8}-z^{8}-5a^{6}z^{6}+15a^{4}z^{6}+14a^{2}z^{6}-5z^{6}-10a^{6}z^{4}+19a^{4}z^{4}+14a^{2}z^{4}-9z^{4}-8a^{6}z^{2}+12a^{4}z^{2}+6a^{2}z^{2}-6z^{2}-2a^{6}+2a^{4}+2a^{2}-1$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 3 \text{QuantumGroups$\grave{ }$a}^5 z^{13}+3 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+9 \text{QuantumGroups$\grave{ }$a}^6 z^{12}+19 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+10 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+14 \text{QuantumGroups$\grave{ }$a}^7 z^{11}+20 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+21 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+15 \text{QuantumGroups$\grave{ }$a} z^{11}+14 \text{QuantumGroups$\grave{ }$a}^8 z^{10}+\text{QuantumGroups$\grave{ }$a}^6 z^{10}-38 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-11 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+14 z^{10}+9 \text{QuantumGroups$\grave{ }$a}^9 z^9-22 \text{QuantumGroups$\grave{ }$a}^7 z^9-57 \text{QuantumGroups$\grave{ }$a}^5 z^9-75 \text{QuantumGroups$\grave{ }$a}^3 z^9-40 \text{QuantumGroups$\grave{ }$a} z^9+9 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^{10} z^8-31 \text{QuantumGroups$\grave{ }$a}^8 z^8-32 \text{QuantumGroups$\grave{ }$a}^6 z^8+36 \text{QuantumGroups$\grave{ }$a}^4 z^8-12 \text{QuantumGroups$\grave{ }$a}^2 z^8+4 z^8 $Failed^{-1} -41 z^8+\text{QuantumGroups$\grave{ }$a}^{11} z^7-20 \text{QuantumGroups$\grave{ }$a}^9 z^7+6 \text{QuantumGroups$\grave{ }$a}^7 z^7+60 \text{QuantumGroups$\grave{ }$a}^5 z^7+110 \text{QuantumGroups$\grave{ }$a}^3 z^7+51 \text{QuantumGroups$\grave{ }$a} z^7-25 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^{10} z^6+28 \text{QuantumGroups$\grave{ }$a}^8 z^6+34 \text{QuantumGroups$\grave{ }$a}^6 z^6-27 \text{QuantumGroups$\grave{ }$a}^4 z^6+40 \text{QuantumGroups$\grave{ }$a}^2 z^6-11 z^6 $Failed^{-1} +52 z^6-3 \text{QuantumGroups$\grave{ }$a}^{11} z^5+14 \text{QuantumGroups$\grave{ }$a}^9 z^5+2 \text{QuantumGroups$\grave{ }$a}^7 z^5-35 \text{QuantumGroups$\grave{ }$a}^5 z^5-79 \text{QuantumGroups$\grave{ }$a}^3 z^5-34 \text{QuantumGroups$\grave{ }$a} z^5+22 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^{10} z^4-19 \text{QuantumGroups$\grave{ }$a}^8 z^4-14 \text{QuantumGroups$\grave{ }$a}^6 z^4+24 \text{QuantumGroups$\grave{ }$a}^4 z^4-34 \text{QuantumGroups$\grave{ }$a}^2 z^4+7 z^4 $Failed^{-1} -38 z^4+3 \text{QuantumGroups$\grave{ }$a}^{11} z^3-4 \text{QuantumGroups$\grave{ }$a}^9 z^3-6 \text{QuantumGroups$\grave{ }$a}^7 z^3+12 \text{QuantumGroups$\grave{ }$a}^5 z^3+28 \text{QuantumGroups$\grave{ }$a}^3 z^3+7 \text{QuantumGroups$\grave{ }$a} z^3-8 z^3 $Failed^{-1} +2 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^{10} z^2+5 \text{QuantumGroups$\grave{ }$a}^8 z^2-3 \text{QuantumGroups$\grave{ }$a}^6 z^2-11 \text{QuantumGroups$\grave{ }$a}^4 z^2+11 \text{QuantumGroups$\grave{ }$a}^2 z^2+12 z^2-\text{QuantumGroups$\grave{ }$a}^{11} z+\text{QuantumGroups$\grave{ }$a}^9 z+2 \text{QuantumGroups$\grave{ }$a}^7 z-\text{QuantumGroups$\grave{ }$a}^5 z-2 \text{QuantumGroups$\grave{ }$a}^3 z+z $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^6+2 \text{QuantumGroups$\grave{ }$a}^4-2 \text{QuantumGroups$\grave{ }$a}^2-1}

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