K14a837

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a837

Polynomial invariants

Jones polynomial	Data:K14a837/Jones Polynomial
Alexander polynomial	$-t^{5}+7t^{4}-25t^{3}+59t^{2}-98t+117-98t^{-1}+59t^{-2}-25t^{-3}+7t^{-4}-t^{-5}$
Conway polynomial	Data:K14a837/Conway Polynomial
Determinant	Data:K14a837/Determinant
Signature	Data:K14a837/Signature
HOMFLY-PT polynomial	$-z^{10}+a^{2}z^{8}+3z^{8}a^{-2}-7z^{8}+5a^{2}z^{6}+16z^{6}a^{-2}-3z^{6}a^{-4}-22z^{6}+10a^{2}z^{4}+35z^{4}a^{-2}-11z^{4}a^{-4}+z^{4}a^{-6}-36z^{4}+9a^{2}z^{2}+36z^{2}a^{-2}-15z^{2}a^{-4}+2z^{2}a^{-6}-32z^{2}+4a^{2}+15a^{-2}-7a^{-4}+a^{-6}-12$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle z^{13} $Failed^{-1} +z^{13} $Failed^{-1} +11 z^{12} $Failed^{-1} +5 z^{12} $Failed^{-1} +6 z^{12}+14 \text{QuantumGroups$\grave{ }$a} z^{11}+34 z^{11} $Failed^{-1} +30 z^{11} $Failed^{-1} +10 z^{11} $Failed^{-1} +17 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+33 z^{10} $Failed^{-1} +26 z^{10} $Failed^{-1} +10 z^{10} $Failed^{-1} +34 z^{10}+14 \text{QuantumGroups$\grave{ }$a}^3 z^9-5 \text{QuantumGroups$\grave{ }$a} z^9-68 z^9 $Failed^{-1} -64 z^9 $Failed^{-1} -10 z^9 $Failed^{-1} +5 z^9 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^4 z^8-25 \text{QuantumGroups$\grave{ }$a}^2 z^8-187 z^8 $Failed^{-1} -125 z^8 $Failed^{-1} -30 z^8 $Failed^{-1} +z^8 $Failed^{-1} -127 z^8+4 \text{QuantumGroups$\grave{ }$a}^5 z^7-21 \text{QuantumGroups$\grave{ }$a}^3 z^7-32 \text{QuantumGroups$\grave{ }$a} z^7-z^7 $Failed^{-1} -22 z^7 $Failed^{-1} -45 z^7 $Failed^{-1} -17 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^6-15 \text{QuantumGroups$\grave{ }$a}^4 z^6+19 \text{QuantumGroups$\grave{ }$a}^2 z^6+270 z^6 $Failed^{-1} +163 z^6 $Failed^{-1} +29 z^6 $Failed^{-1} -3 z^6 $Failed^{-1} +174 z^6-7 \text{QuantumGroups$\grave{ }$a}^5 z^5+13 \text{QuantumGroups$\grave{ }$a}^3 z^5+50 \text{QuantumGroups$\grave{ }$a} z^5+81 z^5 $Failed^{-1} +114 z^5 $Failed^{-1} +84 z^5 $Failed^{-1} +21 z^5 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6 z^4+10 \text{QuantumGroups$\grave{ }$a}^4 z^4-13 \text{QuantumGroups$\grave{ }$a}^2 z^4-196 z^4 $Failed^{-1} -105 z^4 $Failed^{-1} -12 z^4 $Failed^{-1} +3 z^4 $Failed^{-1} -131 z^4+4 \text{QuantumGroups$\grave{ }$a}^5 z^3-4 \text{QuantumGroups$\grave{ }$a}^3 z^3-30 \text{QuantumGroups$\grave{ }$a} z^3-64 z^3 $Failed^{-1} -83 z^3 $Failed^{-1} -52 z^3 $Failed^{-1} -11 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^2-3 \text{QuantumGroups$\grave{ }$a}^4 z^2+10 \text{QuantumGroups$\grave{ }$a}^2 z^2+80 z^2 $Failed^{-1} +40 z^2 $Failed^{-1} +4 z^2 $Failed^{-1} -z^2 $Failed^{-1} +59 z^2-\text{QuantumGroups$\grave{ }$a}^5 z+\text{QuantumGroups$\grave{ }$a}^3 z+8 \text{QuantumGroups$\grave{ }$a} z+16 z $Failed^{-1} +19 z $Failed^{-1} +11 z $Failed^{-1} +2 z $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^2-15 $Failed^{-1} -7 $Failed^{-1} - $Failed^{-1} -12}

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