K14a13278

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13278

Polynomial invariants

Jones polynomial	Data:K14a13278/Jones Polynomial
Alexander polynomial	$t^{5}-8t^{4}+31t^{3}-73t^{2}+118t-137+118t^{-1}-73t^{-2}+31t^{-3}-8t^{-4}+t^{-5}$
Conway polynomial	Data:K14a13278/Conway Polynomial
Determinant	Data:K14a13278/Determinant
Signature	Data:K14a13278/Signature
HOMFLY-PT polynomial	$a^{2}z^{10}-a^{4}z^{8}+6a^{2}z^{8}-3z^{8}-4a^{4}z^{6}+16a^{2}z^{6}+3z^{6}a^{-2}-13z^{6}-6a^{4}z^{4}+21a^{2}z^{4}+9z^{4}a^{-2}-z^{4}a^{-4}-20z^{4}-4a^{4}z^{2}+12a^{2}z^{2}+8z^{2}a^{-2}-2z^{2}a^{-4}-12z^{2}-a^{4}+2a^{2}+2a^{-2}-a^{-4}-1$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 4 \text{QuantumGroups$\grave{ }$a} z^{13}+4 z^{13} $Failed^{-1} +19 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+11 z^{12} $Failed^{-1} +30 z^{12}+40 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+60 \text{QuantumGroups$\grave{ }$a} z^{11}+31 z^{11} $Failed^{-1} +11 z^{11} $Failed^{-1} +50 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+25 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-20 z^{10} $Failed^{-1} +5 z^{10} $Failed^{-1} -50 z^{10}+43 \text{QuantumGroups$\grave{ }$a}^5 z^9-63 \text{QuantumGroups$\grave{ }$a}^3 z^9-218 \text{QuantumGroups$\grave{ }$a} z^9-154 z^9 $Failed^{-1} -41 z^9 $Failed^{-1} +z^9 $Failed^{-1} +28 \text{QuantumGroups$\grave{ }$a}^6 z^8-103 \text{QuantumGroups$\grave{ }$a}^4 z^8-214 \text{QuantumGroups$\grave{ }$a}^2 z^8-38 z^8 $Failed^{-1} -20 z^8 $Failed^{-1} -101 z^8+14 \text{QuantumGroups$\grave{ }$a}^7 z^7-74 \text{QuantumGroups$\grave{ }$a}^5 z^7-28 \text{QuantumGroups$\grave{ }$a}^3 z^7+203 \text{QuantumGroups$\grave{ }$a} z^7+198 z^7 $Failed^{-1} +51 z^7 $Failed^{-1} -4 z^7 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^8 z^6-33 \text{QuantumGroups$\grave{ }$a}^6 z^6+71 \text{QuantumGroups$\grave{ }$a}^4 z^6+272 \text{QuantumGroups$\grave{ }$a}^2 z^6+107 z^6 $Failed^{-1} +30 z^6 $Failed^{-1} +240 z^6+\text{QuantumGroups$\grave{ }$a}^9 z^5-9 \text{QuantumGroups$\grave{ }$a}^7 z^5+45 \text{QuantumGroups$\grave{ }$a}^5 z^5+68 \text{QuantumGroups$\grave{ }$a}^3 z^5-48 \text{QuantumGroups$\grave{ }$a} z^5-90 z^5 $Failed^{-1} -23 z^5 $Failed^{-1} +6 z^5 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8 z^4+13 \text{QuantumGroups$\grave{ }$a}^6 z^4-32 \text{QuantumGroups$\grave{ }$a}^4 z^4-140 \text{QuantumGroups$\grave{ }$a}^2 z^4-80 z^4 $Failed^{-1} -21 z^4 $Failed^{-1} -153 z^4+2 \text{QuantumGroups$\grave{ }$a}^7 z^3-14 \text{QuantumGroups$\grave{ }$a}^5 z^3-29 \text{QuantumGroups$\grave{ }$a}^3 z^3-4 \text{QuantumGroups$\grave{ }$a} z^3+15 z^3 $Failed^{-1} +2 z^3 $Failed^{-1} -4 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6 z^2+10 \text{QuantumGroups$\grave{ }$a}^4 z^2+32 \text{QuantumGroups$\grave{ }$a}^2 z^2+23 z^2 $Failed^{-1} +7 z^2 $Failed^{-1} +37 z^2+2 \text{QuantumGroups$\grave{ }$a}^5 z+3 \text{QuantumGroups$\grave{ }$a}^3 z-2 z $Failed^{-1} +z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^4-2 \text{QuantumGroups$\grave{ }$a}^2-2 $Failed^{-1} - $Failed^{-1} -1}

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