K14a18328

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18328

Polynomial invariants

Jones polynomial	Data:K14a18328/Jones Polynomial
Alexander polynomial	$-2t^{5}+10t^{4}-25t^{3}+45t^{2}-64t+73-64t^{-1}+45t^{-2}-25t^{-3}+10t^{-4}-2t^{-5}$
Conway polynomial	Data:K14a18328/Conway Polynomial
Determinant	Data:K14a18328/Determinant
Signature	Data:K14a18328/Signature
HOMFLY-PT polynomial	$-a^{2}z^{10}-z^{10}+a^{4}z^{8}-6a^{2}z^{8}+z^{8}a^{-2}-6z^{8}+5a^{4}z^{6}-12a^{2}z^{6}+5z^{6}a^{-2}-13z^{6}+7a^{4}z^{4}-7a^{2}z^{4}+8z^{4}a^{-2}-13z^{4}+a^{4}z^{2}+4a^{2}z^{2}+4z^{2}a^{-2}-8z^{2}-2a^{4}+5a^{2}+a^{-2}-3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 3 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+3 \text{QuantumGroups$\grave{ }$a} z^{13}+7 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+16 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+9 z^{12}+8 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+2 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+8 \text{QuantumGroups$\grave{ }$a} z^{11}+14 z^{11} $Failed^{-1} +7 \text{QuantumGroups$\grave{ }$a}^6 z^{10}-22 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-65 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+16 z^{10} $Failed^{-1} -20 z^{10}+4 \text{QuantumGroups$\grave{ }$a}^7 z^9-26 \text{QuantumGroups$\grave{ }$a}^5 z^9-33 \text{QuantumGroups$\grave{ }$a}^3 z^9-55 \text{QuantumGroups$\grave{ }$a} z^9-38 z^9 $Failed^{-1} +14 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^8-27 \text{QuantumGroups$\grave{ }$a}^6 z^8+25 \text{QuantumGroups$\grave{ }$a}^4 z^8+120 \text{QuantumGroups$\grave{ }$a}^2 z^8-43 z^8 $Failed^{-1} +9 z^8 $Failed^{-1} +15 z^8-17 \text{QuantumGroups$\grave{ }$a}^7 z^7+16 \text{QuantumGroups$\grave{ }$a}^5 z^7+60 \text{QuantumGroups$\grave{ }$a}^3 z^7+112 \text{QuantumGroups$\grave{ }$a} z^7+46 z^7 $Failed^{-1} -35 z^7 $Failed^{-1} +4 z^7 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^8 z^6+28 \text{QuantumGroups$\grave{ }$a}^6 z^6-25 \text{QuantumGroups$\grave{ }$a}^4 z^6-112 \text{QuantumGroups$\grave{ }$a}^2 z^6+49 z^6 $Failed^{-1} -20 z^6 $Failed^{-1} +z^6 $Failed^{-1} +15 z^6+21 \text{QuantumGroups$\grave{ }$a}^7 z^5+12 \text{QuantumGroups$\grave{ }$a}^5 z^5-48 \text{QuantumGroups$\grave{ }$a}^3 z^5-96 \text{QuantumGroups$\grave{ }$a} z^5-17 z^5 $Failed^{-1} +32 z^5 $Failed^{-1} -8 z^5 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^8 z^4-7 \text{QuantumGroups$\grave{ }$a}^6 z^4+16 \text{QuantumGroups$\grave{ }$a}^4 z^4+38 \text{QuantumGroups$\grave{ }$a}^2 z^4-21 z^4 $Failed^{-1} +12 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} -24 z^4-9 \text{QuantumGroups$\grave{ }$a}^7 z^3-15 \text{QuantumGroups$\grave{ }$a}^5 z^3+10 \text{QuantumGroups$\grave{ }$a}^3 z^3+27 \text{QuantumGroups$\grave{ }$a} z^3-z^3 $Failed^{-1} -10 z^3 $Failed^{-1} +2 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8 z^2-\text{QuantumGroups$\grave{ }$a}^6 z^2+5 \text{QuantumGroups$\grave{ }$a}^2 z^2+4 z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +11 z^2+\text{QuantumGroups$\grave{ }$a}^7 z+4 \text{QuantumGroups$\grave{ }$a}^5 z+3 \text{QuantumGroups$\grave{ }$a}^3 z+z $Failed^{-1} +z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4-5 \text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} -3}

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