K14a7223

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a7223

Polynomial invariants

Jones polynomial	Data:K14a7223/Jones Polynomial
Alexander polynomial	$4t^{4}-17t^{3}+38t^{2}-56t+63-56t^{-1}+38t^{-2}-17t^{-3}+4t^{-4}$
Conway polynomial	Data:K14a7223/Conway Polynomial
Determinant	Data:K14a7223/Determinant
Signature	Data:K14a7223/Signature
HOMFLY-PT polynomial	$2z^{8}a^{-2}+z^{8}a^{-4}+z^{8}-a^{2}z^{6}+9z^{6}a^{-2}+4z^{6}a^{-4}-z^{6}a^{-6}+4z^{6}-4a^{2}z^{4}+12z^{4}a^{-2}+6z^{4}a^{-4}-4z^{4}a^{-6}+6z^{4}-5a^{2}z^{2}+4z^{2}a^{-2}+7z^{2}a^{-4}-5z^{2}a^{-6}+6z^{2}-2a^{2}-a^{-2}+4a^{-4}-3a^{-6}+3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle z^{13} $Failed^{-1} +z^{13} $Failed^{-1} +4 z^{12} $Failed^{-1} +8 z^{12} $Failed^{-1} +4 z^{12} $Failed^{-1} +8 z^{11} $Failed^{-1} +13 z^{11} $Failed^{-1} +10 z^{11} $Failed^{-1} +5 z^{11} $Failed^{-1} +6 z^{10} $Failed^{-1} -21 z^{10} $Failed^{-1} -13 z^{10} $Failed^{-1} +3 z^{10} $Failed^{-1} +11 z^{10}+12 \text{QuantumGroups$\grave{ }$a} z^9-6 z^9 $Failed^{-1} -51 z^9 $Failed^{-1} -59 z^9 $Failed^{-1} -25 z^9 $Failed^{-1} +z^9 $Failed^{-1} +10 \text{QuantumGroups$\grave{ }$a}^2 z^8-39 z^8 $Failed^{-1} +7 z^8 $Failed^{-1} +6 z^8 $Failed^{-1} -16 z^8 $Failed^{-1} -14 z^8+6 \text{QuantumGroups$\grave{ }$a}^3 z^7-20 \text{QuantumGroups$\grave{ }$a} z^7-18 z^7 $Failed^{-1} +65 z^7 $Failed^{-1} +106 z^7 $Failed^{-1} +43 z^7 $Failed^{-1} -6 z^7 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^4 z^6-17 \text{QuantumGroups$\grave{ }$a}^2 z^6+38 z^6 $Failed^{-1} +2 z^6 $Failed^{-1} +5 z^6 $Failed^{-1} +28 z^6 $Failed^{-1} -7 z^6+\text{QuantumGroups$\grave{ }$a}^5 z^5-7 \text{QuantumGroups$\grave{ }$a}^3 z^5+14 \text{QuantumGroups$\grave{ }$a} z^5+21 z^5 $Failed^{-1} -56 z^5 $Failed^{-1} -102 z^5 $Failed^{-1} -35 z^5 $Failed^{-1} +12 z^5 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^4 z^4+18 \text{QuantumGroups$\grave{ }$a}^2 z^4-14 z^4 $Failed^{-1} +8 z^4 $Failed^{-1} +6 z^4 $Failed^{-1} -18 z^4 $Failed^{-1} +24 z^4-2 \text{QuantumGroups$\grave{ }$a}^5 z^3+3 \text{QuantumGroups$\grave{ }$a}^3 z^3+\text{QuantumGroups$\grave{ }$a} z^3-8 z^3 $Failed^{-1} +28 z^3 $Failed^{-1} +60 z^3 $Failed^{-1} +19 z^3 $Failed^{-1} -9 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^2-9 \text{QuantumGroups$\grave{ }$a}^2 z^2-3 z^2 $Failed^{-1} -10 z^2 $Failed^{-1} -8 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} -14 z^2+\text{QuantumGroups$\grave{ }$a}^5 z-\text{QuantumGroups$\grave{ }$a}^3 z-2 \text{QuantumGroups$\grave{ }$a} z-6 z $Failed^{-1} -14 z $Failed^{-1} -6 z $Failed^{-1} +2 z $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} +4 $Failed^{-1} +3 $Failed^{-1} +3}

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