K14a7319

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a7319

Polynomial invariants

Jones polynomial	Data:K14a7319/Jones Polynomial
Alexander polynomial	$-t^{5}+7t^{4}-24t^{3}+54t^{2}-85t+99-85t^{-1}+54t^{-2}-24t^{-3}+7t^{-4}-t^{-5}$
Conway polynomial	Data:K14a7319/Conway Polynomial
Determinant	Data:K14a7319/Determinant
Signature	Data:K14a7319/Signature
HOMFLY-PT polynomial	$-z^{10}+2a^{2}z^{8}+2z^{8}a^{-2}-7z^{8}-a^{4}z^{6}+11a^{2}z^{6}+10z^{6}a^{-2}-z^{6}a^{-4}-22z^{6}-4a^{4}z^{4}+24a^{2}z^{4}+18z^{4}a^{-2}-3z^{4}a^{-4}-35z^{4}-6a^{4}z^{2}+23a^{2}z^{2}+12z^{2}a^{-2}-2z^{2}a^{-4}-25z^{2}-3a^{4}+7a^{2}+a^{-2}-4$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle \text{QuantumGroups$\grave{ }$a} z^{13}+z^{13} $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+5 z^{12} $Failed^{-1} +10 z^{12}+10 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+24 \text{QuantumGroups$\grave{ }$a} z^{11}+25 z^{11} $Failed^{-1} +11 z^{11} $Failed^{-1} +11 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+15 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+21 z^{10} $Failed^{-1} +14 z^{10} $Failed^{-1} +11 z^{10}+8 \text{QuantumGroups$\grave{ }$a}^5 z^9-13 \text{QuantumGroups$\grave{ }$a}^3 z^9-64 \text{QuantumGroups$\grave{ }$a} z^9-63 z^9 $Failed^{-1} -9 z^9 $Failed^{-1} +11 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^8-24 \text{QuantumGroups$\grave{ }$a}^4 z^8-73 \text{QuantumGroups$\grave{ }$a}^2 z^8-97 z^8 $Failed^{-1} -34 z^8 $Failed^{-1} +5 z^8 $Failed^{-1} -103 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-19 \text{QuantumGroups$\grave{ }$a}^5 z^7-6 \text{QuantumGroups$\grave{ }$a}^3 z^7+58 \text{QuantumGroups$\grave{ }$a} z^7+37 z^7 $Failed^{-1} -39 z^7 $Failed^{-1} -31 z^7 $Failed^{-1} +z^7 $Failed^{-1} -11 \text{QuantumGroups$\grave{ }$a}^6 z^6+18 \text{QuantumGroups$\grave{ }$a}^4 z^6+114 \text{QuantumGroups$\grave{ }$a}^2 z^6+134 z^6 $Failed^{-1} +22 z^6 $Failed^{-1} -13 z^6 $Failed^{-1} +184 z^6-3 \text{QuantumGroups$\grave{ }$a}^7 z^5+12 \text{QuantumGroups$\grave{ }$a}^5 z^5+15 \text{QuantumGroups$\grave{ }$a}^3 z^5-3 \text{QuantumGroups$\grave{ }$a} z^5+35 z^5 $Failed^{-1} +66 z^5 $Failed^{-1} +26 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^6 z^4-15 \text{QuantumGroups$\grave{ }$a}^4 z^4-95 \text{QuantumGroups$\grave{ }$a}^2 z^4-81 z^4 $Failed^{-1} -6 z^4 $Failed^{-1} +7 z^4 $Failed^{-1} -139 z^4+3 \text{QuantumGroups$\grave{ }$a}^7 z^3-3 \text{QuantumGroups$\grave{ }$a}^5 z^3-14 \text{QuantumGroups$\grave{ }$a}^3 z^3-21 \text{QuantumGroups$\grave{ }$a} z^3-37 z^3 $Failed^{-1} -33 z^3 $Failed^{-1} -9 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6 z^2+10 \text{QuantumGroups$\grave{ }$a}^4 z^2+40 \text{QuantumGroups$\grave{ }$a}^2 z^2+23 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} +48 z^2-\text{QuantumGroups$\grave{ }$a}^7 z+\text{QuantumGroups$\grave{ }$a}^5 z+5 \text{QuantumGroups$\grave{ }$a}^3 z+7 \text{QuantumGroups$\grave{ }$a} z+6 z $Failed^{-1} +2 z $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4-7 \text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} -4}

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