K14a921

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a921

Polynomial invariants

Jones polynomial	Data:K14a921/Jones Polynomial
Alexander polynomial	$-t^{5}+8t^{4}-30t^{3}+72t^{2}-119t+141-119t^{-1}+72t^{-2}-30t^{-3}+8t^{-4}-t^{-5}$
Conway polynomial	Data:K14a921/Conway Polynomial
Determinant	Data:K14a921/Determinant
Signature	Data:K14a921/Signature
HOMFLY-PT polynomial	$-z^{10}+2a^{2}z^{8}+2z^{8}a^{-2}-6z^{8}-a^{4}z^{6}+10a^{2}z^{6}+8z^{6}a^{-2}-z^{6}a^{-4}-17z^{6}-4a^{4}z^{4}+21a^{2}z^{4}+12z^{4}a^{-2}-2z^{4}a^{-4}-25z^{4}-6a^{4}z^{2}+20a^{2}z^{2}+7z^{2}a^{-2}-z^{2}a^{-4}-18z^{2}-3a^{4}+7a^{2}+a^{-2}-4$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a} z^{13}+2 z^{13} $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+10 z^{12} $Failed^{-1} +19 z^{12}+15 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+41 \text{QuantumGroups$\grave{ }$a} z^{11}+47 z^{11} $Failed^{-1} +21 z^{11} $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+17 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+38 z^{10} $Failed^{-1} +24 z^{10} $Failed^{-1} +17 z^{10}+9 \text{QuantumGroups$\grave{ }$a}^5 z^9-22 \text{QuantumGroups$\grave{ }$a}^3 z^9-108 \text{QuantumGroups$\grave{ }$a} z^9-108 z^9 $Failed^{-1} -15 z^9 $Failed^{-1} +16 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^8-29 \text{QuantumGroups$\grave{ }$a}^4 z^8-89 \text{QuantumGroups$\grave{ }$a}^2 z^8-154 z^8 $Failed^{-1} -47 z^8 $Failed^{-1} +6 z^8 $Failed^{-1} -157 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-20 \text{QuantumGroups$\grave{ }$a}^5 z^7+8 \text{QuantumGroups$\grave{ }$a}^3 z^7+105 \text{QuantumGroups$\grave{ }$a} z^7+56 z^7 $Failed^{-1} -54 z^7 $Failed^{-1} -33 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+27 \text{QuantumGroups$\grave{ }$a}^4 z^6+138 \text{QuantumGroups$\grave{ }$a}^2 z^6+171 z^6 $Failed^{-1} +24 z^6 $Failed^{-1} -10 z^6 $Failed^{-1} +238 z^6-3 \text{QuantumGroups$\grave{ }$a}^7 z^5+15 \text{QuantumGroups$\grave{ }$a}^5 z^5+4 \text{QuantumGroups$\grave{ }$a}^3 z^5-35 \text{QuantumGroups$\grave{ }$a} z^5+24 z^5 $Failed^{-1} +67 z^5 $Failed^{-1} +21 z^5 $Failed^{-1} -z^5 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^6 z^4-22 \text{QuantumGroups$\grave{ }$a}^4 z^4-110 \text{QuantumGroups$\grave{ }$a}^2 z^4-85 z^4 $Failed^{-1} -7 z^4 $Failed^{-1} +4 z^4 $Failed^{-1} -154 z^4+3 \text{QuantumGroups$\grave{ }$a}^7 z^3-5 \text{QuantumGroups$\grave{ }$a}^5 z^3-9 \text{QuantumGroups$\grave{ }$a}^3 z^3-6 \text{QuantumGroups$\grave{ }$a} z^3-22 z^3 $Failed^{-1} -23 z^3 $Failed^{-1} -6 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6 z^2+13 \text{QuantumGroups$\grave{ }$a}^4 z^2+43 \text{QuantumGroups$\grave{ }$a}^2 z^2+20 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} +45 z^2-\text{QuantumGroups$\grave{ }$a}^7 z+\text{QuantumGroups$\grave{ }$a}^5 z+4 \text{QuantumGroups$\grave{ }$a}^3 z+4 \text{QuantumGroups$\grave{ }$a} z+3 z $Failed^{-1} +z $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4-7 \text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} -4}

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