K14a13521

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13521

Polynomial invariants

Jones polynomial	Data:K14a13521/Jones Polynomial
Alexander polynomial	$-t^{5}+8t^{4}-31t^{3}+75t^{2}-124t+147-124t^{-1}+75t^{-2}-31t^{-3}+8t^{-4}-t^{-5}$
Conway polynomial	Data:K14a13521/Conway Polynomial
Determinant	Data:K14a13521/Determinant
Signature	Data:K14a13521/Signature
HOMFLY-PT polynomial	$-z^{10}+3a^{2}z^{8}+z^{8}a^{-2}-6z^{8}-3a^{4}z^{6}+13a^{2}z^{6}+4z^{6}a^{-2}-16z^{6}+a^{6}z^{4}-9a^{4}z^{4}+21a^{2}z^{4}+6z^{4}a^{-2}-20z^{4}+2a^{6}z^{2}-9a^{4}z^{2}+14a^{2}z^{2}+3z^{2}a^{-2}-10z^{2}+a^{6}-3a^{4}+3a^{2}$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 4 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+4 \text{QuantumGroups$\grave{ }$a} z^{13}+13 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+30 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+17 z^{12}+17 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+40 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+54 \text{QuantumGroups$\grave{ }$a} z^{11}+31 z^{11} $Failed^{-1} +12 \text{QuantumGroups$\grave{ }$a}^6 z^{10}-6 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-37 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+33 z^{10} $Failed^{-1} +14 z^{10}+5 \text{QuantumGroups$\grave{ }$a}^7 z^9-43 \text{QuantumGroups$\grave{ }$a}^5 z^9-149 \text{QuantumGroups$\grave{ }$a}^3 z^9-179 \text{QuantumGroups$\grave{ }$a} z^9-54 z^9 $Failed^{-1} +24 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^8-35 \text{QuantumGroups$\grave{ }$a}^6 z^8-69 \text{QuantumGroups$\grave{ }$a}^4 z^8-88 \text{QuantumGroups$\grave{ }$a}^2 z^8-69 z^8 $Failed^{-1} +13 z^8 $Failed^{-1} -137 z^8-15 \text{QuantumGroups$\grave{ }$a}^7 z^7+29 \text{QuantumGroups$\grave{ }$a}^5 z^7+169 \text{QuantumGroups$\grave{ }$a}^3 z^7+190 \text{QuantumGroups$\grave{ }$a} z^7+18 z^7 $Failed^{-1} -42 z^7 $Failed^{-1} +5 z^7 $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^8 z^6+34 \text{QuantumGroups$\grave{ }$a}^6 z^6+109 \text{QuantumGroups$\grave{ }$a}^4 z^6+189 \text{QuantumGroups$\grave{ }$a}^2 z^6+63 z^6 $Failed^{-1} -18 z^6 $Failed^{-1} +z^6 $Failed^{-1} +199 z^6+15 \text{QuantumGroups$\grave{ }$a}^7 z^5-8 \text{QuantumGroups$\grave{ }$a}^5 z^5-92 \text{QuantumGroups$\grave{ }$a}^3 z^5-78 \text{QuantumGroups$\grave{ }$a} z^5+25 z^5 $Failed^{-1} +28 z^5 $Failed^{-1} -6 z^5 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^8 z^4-17 \text{QuantumGroups$\grave{ }$a}^6 z^4-76 \text{QuantumGroups$\grave{ }$a}^4 z^4-130 \text{QuantumGroups$\grave{ }$a}^2 z^4-28 z^4 $Failed^{-1} +6 z^4 $Failed^{-1} -z^4 $Failed^{-1} -109 z^4-6 \text{QuantumGroups$\grave{ }$a}^7 z^3+\text{QuantumGroups$\grave{ }$a}^5 z^3+25 \text{QuantumGroups$\grave{ }$a}^3 z^3+16 \text{QuantumGroups$\grave{ }$a} z^3-12 z^3 $Failed^{-1} -9 z^3 $Failed^{-1} +z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8 z^2+6 \text{QuantumGroups$\grave{ }$a}^6 z^2+25 \text{QuantumGroups$\grave{ }$a}^4 z^2+36 \text{QuantumGroups$\grave{ }$a}^2 z^2+5 z^2 $Failed^{-1} -z^2 $Failed^{-1} +24 z^2+\text{QuantumGroups$\grave{ }$a}^7 z-4 \text{QuantumGroups$\grave{ }$a}^3 z-4 \text{QuantumGroups$\grave{ }$a} z-z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6-3 \text{QuantumGroups$\grave{ }$a}^4-3 \text{QuantumGroups$\grave{ }$a}^2}

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