K14a1117

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a1117

Polynomial invariants

Jones polynomial	Data:K14a1117/Jones Polynomial
Alexander polynomial	$-9t^{3}+50t^{2}-117t+153-117t^{-1}+50t^{-2}-9t^{-3}$
Conway polynomial	Data:K14a1117/Conway Polynomial
Determinant	Data:K14a1117/Determinant
Signature	Data:K14a1117/Signature
HOMFLY-PT polynomial	$-z^{2}a^{6}-a^{6}+3z^{4}a^{4}+4z^{2}a^{4}+a^{4}-2z^{6}a^{2}+4z^{2}a^{2}+3a^{2}-5z^{6}-12z^{4}-14z^{2}-6-2z^{6}a^{-2}+2z^{4}a^{-2}+9z^{2}a^{-2}+6a^{-2}+3z^{4}a^{-4}+z^{2}a^{-4}-2a^{-4}-z^{2}a^{-6}$
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a} z^{13}+2 z^{13} $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+9 z^{12} $Failed^{-1} +17 z^{12}+12 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+30 \text{QuantumGroups$\grave{ }$a} z^{11}+35 z^{11} $Failed^{-1} +17 z^{11} $Failed^{-1} +11 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+4 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+16 z^{10} $Failed^{-1} +18 z^{10} $Failed^{-1} -9 z^{10}+8 \text{QuantumGroups$\grave{ }$a}^5 z^9-19 \text{QuantumGroups$\grave{ }$a}^3 z^9-100 \text{QuantumGroups$\grave{ }$a} z^9-112 z^9 $Failed^{-1} -27 z^9 $Failed^{-1} +12 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^8-19 \text{QuantumGroups$\grave{ }$a}^4 z^8-50 \text{QuantumGroups$\grave{ }$a}^2 z^8-109 z^8 $Failed^{-1} -42 z^8 $Failed^{-1} +5 z^8 $Failed^{-1} -89 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-18 \text{QuantumGroups$\grave{ }$a}^5 z^7+5 \text{QuantumGroups$\grave{ }$a}^3 z^7+129 \text{QuantumGroups$\grave{ }$a} z^7+123 z^7 $Failed^{-1} -11 z^7 $Failed^{-1} -28 z^7 $Failed^{-1} +z^7 $Failed^{-1} -11 \text{QuantumGroups$\grave{ }$a}^6 z^6+\text{QuantumGroups$\grave{ }$a}^4 z^6+81 \text{QuantumGroups$\grave{ }$a}^2 z^6+165 z^6 $Failed^{-1} +31 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +192 z^6-3 \text{QuantumGroups$\grave{ }$a}^7 z^5+10 \text{QuantumGroups$\grave{ }$a}^5 z^5+2 \text{QuantumGroups$\grave{ }$a}^3 z^5-69 \text{QuantumGroups$\grave{ }$a} z^5-44 z^5 $Failed^{-1} +35 z^5 $Failed^{-1} +19 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +10 \text{QuantumGroups$\grave{ }$a}^6 z^4+9 \text{QuantumGroups$\grave{ }$a}^4 z^4-60 \text{QuantumGroups$\grave{ }$a}^2 z^4-112 z^4 $Failed^{-1} -19 z^4 $Failed^{-1} +6 z^4 $Failed^{-1} -146 z^4+3 \text{QuantumGroups$\grave{ }$a}^7 z^3-\text{QuantumGroups$\grave{ }$a}^5 z^3-5 \text{QuantumGroups$\grave{ }$a}^3 z^3+14 \text{QuantumGroups$\grave{ }$a} z^3+4 z^3 $Failed^{-1} -21 z^3 $Failed^{-1} -9 z^3 $Failed^{-1} +z^3 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^6 z^2-6 \text{QuantumGroups$\grave{ }$a}^4 z^2+19 \text{QuantumGroups$\grave{ }$a}^2 z^2+39 z^2 $Failed^{-1} +8 z^2 $Failed^{-1} -z^2 $Failed^{-1} +51 z^2-\text{QuantumGroups$\grave{ }$a}^7 z+\text{QuantumGroups$\grave{ }$a}^3 z-\text{QuantumGroups$\grave{ }$a} z+3 z $Failed^{-1} +2 z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6+\text{QuantumGroups$\grave{ }$a}^4-3 \text{QuantumGroups$\grave{ }$a}^2-6 $Failed^{-1} -2 $Failed^{-1} -6}

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