K14a18472

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18472

Polynomial invariants

Jones polynomial	Data:K14a18472/Jones Polynomial
Alexander polynomial	$3t^{4}-11t^{3}+20t^{2}-26t+29-26t^{-1}+20t^{-2}-11t^{-3}+3t^{-4}$
Conway polynomial	Data:K14a18472/Conway Polynomial
Determinant	Data:K14a18472/Determinant
Signature	Data:K14a18472/Signature
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}a^{-4}+z^{8}-a^{2}z^{6}+4z^{6}a^{-2}+5z^{6}a^{-4}-z^{6}a^{-6}+6z^{6}-5a^{2}z^{4}+2z^{4}a^{-2}+8z^{4}a^{-4}-4z^{4}a^{-6}+13z^{4}-7a^{2}z^{2}-5z^{2}a^{-2}+6z^{2}a^{-4}-4z^{2}a^{-6}+13z^{2}-2a^{2}-3a^{-2}+2a^{-4}-a^{-6}+5$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle \text{QuantumGroups$\grave{ }$a} z^{13}+z^{13} $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+4 z^{12} $Failed^{-1} +6 z^{12}+\text{QuantumGroups$\grave{ }$a}^3 z^{11}-3 \text{QuantumGroups$\grave{ }$a} z^{11}+4 z^{11} $Failed^{-1} +8 z^{11} $Failed^{-1} -17 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-13 z^{10} $Failed^{-1} +12 z^{10} $Failed^{-1} -42 z^{10}-9 \text{QuantumGroups$\grave{ }$a}^3 z^9-16 \text{QuantumGroups$\grave{ }$a} z^9-53 z^9 $Failed^{-1} -31 z^9 $Failed^{-1} +15 z^9 $Failed^{-1} +54 \text{QuantumGroups$\grave{ }$a}^2 z^8-10 z^8 $Failed^{-1} -44 z^8 $Failed^{-1} +16 z^8 $Failed^{-1} +104 z^8+30 \text{QuantumGroups$\grave{ }$a}^3 z^7+82 \text{QuantumGroups$\grave{ }$a} z^7+135 z^7 $Failed^{-1} +20 z^7 $Failed^{-1} -49 z^7 $Failed^{-1} +14 z^7 $Failed^{-1} -80 \text{QuantumGroups$\grave{ }$a}^2 z^6+55 z^6 $Failed^{-1} +34 z^6 $Failed^{-1} -45 z^6 $Failed^{-1} +10 z^6 $Failed^{-1} -114 z^6-45 \text{QuantumGroups$\grave{ }$a}^3 z^5-124 \text{QuantumGroups$\grave{ }$a} z^5-127 z^5 $Failed^{-1} +23 z^5 $Failed^{-1} +35 z^5 $Failed^{-1} -30 z^5 $Failed^{-1} +6 z^5 $Failed^{-1} +57 \text{QuantumGroups$\grave{ }$a}^2 z^4-31 z^4 $Failed^{-1} +6 z^4 $Failed^{-1} +29 z^4 $Failed^{-1} -13 z^4 $Failed^{-1} +3 z^4 $Failed^{-1} +65 z^4+29 \text{QuantumGroups$\grave{ }$a}^3 z^3+72 \text{QuantumGroups$\grave{ }$a} z^3+46 z^3 $Failed^{-1} -17 z^3 $Failed^{-1} -3 z^3 $Failed^{-1} +13 z^3 $Failed^{-1} -3 z^3 $Failed^{-1} +z^3 $Failed^{-1} -18 \text{QuantumGroups$\grave{ }$a}^2 z^2-5 z^2 $Failed^{-1} -7 z^2 $Failed^{-1} -7 z^2 $Failed^{-1} +2 z^2 $Failed^{-1} -25 z^2-6 \text{QuantumGroups$\grave{ }$a}^3 z-13 \text{QuantumGroups$\grave{ }$a} z-7 z $Failed^{-1} +2 z $Failed^{-1} -2 z $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^2+3 $Failed^{-1} +2 $Failed^{-1} + $Failed^{-1} +5}

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