K14a13043

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13043

Polynomial invariants

Jones polynomial	Data:K14a13043/Jones Polynomial
Alexander polynomial	$-t^{5}+8t^{4}-25t^{3}+52t^{2}-80t+93-80t^{-1}+52t^{-2}-25t^{-3}+8t^{-4}-t^{-5}$
Conway polynomial	Data:K14a13043/Conway Polynomial
Determinant	Data:K14a13043/Determinant
Signature	Data:K14a13043/Signature
HOMFLY-PT polynomial	$-z^{10}+2a^{2}z^{8}+2z^{8}a^{-2}-6z^{8}-a^{4}z^{6}+11a^{2}z^{6}+10z^{6}a^{-2}-z^{6}a^{-4}-15z^{6}-5a^{4}z^{4}+23a^{2}z^{4}+19z^{4}a^{-2}-4z^{4}a^{-4}-21z^{4}-8a^{4}z^{2}+22a^{2}z^{2}+17z^{2}a^{-2}-6z^{2}a^{-4}-19z^{2}-4a^{4}+9a^{2}+7a^{-2}-3a^{-4}-8$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a} z^{13}+2 z^{13} $Failed^{-1} +7 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+8 z^{12} $Failed^{-1} +15 z^{12}+10 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+21 \text{QuantumGroups$\grave{ }$a} z^{11}+25 z^{11} $Failed^{-1} +14 z^{11} $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-5 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+4 z^{10} $Failed^{-1} +14 z^{10} $Failed^{-1} -24 z^{10}+6 \text{QuantumGroups$\grave{ }$a}^5 z^9-26 \text{QuantumGroups$\grave{ }$a}^3 z^9-91 \text{QuantumGroups$\grave{ }$a} z^9-98 z^9 $Failed^{-1} -30 z^9 $Failed^{-1} +9 z^9 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^6 z^8-25 \text{QuantumGroups$\grave{ }$a}^4 z^8-33 \text{QuantumGroups$\grave{ }$a}^2 z^8-77 z^8 $Failed^{-1} -37 z^8 $Failed^{-1} +4 z^8 $Failed^{-1} -41 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-16 \text{QuantumGroups$\grave{ }$a}^5 z^7+32 \text{QuantumGroups$\grave{ }$a}^3 z^7+150 \text{QuantumGroups$\grave{ }$a} z^7+132 z^7 $Failed^{-1} +8 z^7 $Failed^{-1} -22 z^7 $Failed^{-1} +z^7 $Failed^{-1} -9 \text{QuantumGroups$\grave{ }$a}^6 z^6+32 \text{QuantumGroups$\grave{ }$a}^4 z^6+95 \text{QuantumGroups$\grave{ }$a}^2 z^6+143 z^6 $Failed^{-1} +36 z^6 $Failed^{-1} -10 z^6 $Failed^{-1} +151 z^6-4 \text{QuantumGroups$\grave{ }$a}^7 z^5+12 \text{QuantumGroups$\grave{ }$a}^5 z^5-22 \text{QuantumGroups$\grave{ }$a}^3 z^5-103 \text{QuantumGroups$\grave{ }$a} z^5-64 z^5 $Failed^{-1} +19 z^5 $Failed^{-1} +15 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +7 \text{QuantumGroups$\grave{ }$a}^6 z^4-34 \text{QuantumGroups$\grave{ }$a}^4 z^4-106 \text{QuantumGroups$\grave{ }$a}^2 z^4-110 z^4 $Failed^{-1} -32 z^4 $Failed^{-1} +6 z^4 $Failed^{-1} -137 z^4+5 \text{QuantumGroups$\grave{ }$a}^7 z^3-4 \text{QuantumGroups$\grave{ }$a}^5 z^3-2 \text{QuantumGroups$\grave{ }$a}^3 z^3+29 \text{QuantumGroups$\grave{ }$a} z^3+15 z^3 $Failed^{-1} -20 z^3 $Failed^{-1} -10 z^3 $Failed^{-1} +3 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6 z^2+19 \text{QuantumGroups$\grave{ }$a}^4 z^2+49 \text{QuantumGroups$\grave{ }$a}^2 z^2+42 z^2 $Failed^{-1} +15 z^2 $Failed^{-1} -z^2 $Failed^{-1} +55 z^2-2 \text{QuantumGroups$\grave{ }$a}^7 z+\text{QuantumGroups$\grave{ }$a}^5 z+3 \text{QuantumGroups$\grave{ }$a}^3 z-3 \text{QuantumGroups$\grave{ }$a} z-2 z $Failed^{-1} +5 z $Failed^{-1} +3 z $Failed^{-1} -z $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^4-9 \text{QuantumGroups$\grave{ }$a}^2-7 $Failed^{-1} -3 $Failed^{-1} -8}

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