K14a1831

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a1831

Polynomial invariants

Jones polynomial	Data:K14a1831/Jones Polynomial
Alexander polynomial	$2t^{4}-17t^{3}+66t^{2}-139t+177-139t^{-1}+66t^{-2}-17t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a1831/Conway Polynomial
Determinant	Data:K14a1831/Determinant
Signature	Data:K14a1831/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}-a^{4}z^{6}+3a^{2}z^{6}-3z^{6}a^{-2}-2a^{4}z^{4}+9a^{2}z^{4}-3z^{4}a^{-2}+3z^{4}a^{-4}-3z^{4}-4a^{4}z^{2}+12a^{2}z^{2}+z^{2}a^{-2}+2z^{2}a^{-4}-z^{2}a^{-6}-6z^{2}-3a^{4}+6a^{2}+2a^{-2}-a^{-4}-3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 3 \text{QuantumGroups$\grave{ }$a} z^{13}+3 z^{13} $Failed^{-1} +13 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+11 z^{12} $Failed^{-1} +24 z^{12}+23 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+46 \text{QuantumGroups$\grave{ }$a} z^{11}+41 z^{11} $Failed^{-1} +18 z^{11} $Failed^{-1} +23 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+16 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+17 z^{10} $Failed^{-1} +18 z^{10} $Failed^{-1} -8 z^{10}+14 \text{QuantumGroups$\grave{ }$a}^5 z^9-36 \text{QuantumGroups$\grave{ }$a}^3 z^9-124 \text{QuantumGroups$\grave{ }$a} z^9-107 z^9 $Failed^{-1} -21 z^9 $Failed^{-1} +12 z^9 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^6 z^8-52 \text{QuantumGroups$\grave{ }$a}^4 z^8-101 \text{QuantumGroups$\grave{ }$a}^2 z^8-91 z^8 $Failed^{-1} -36 z^8 $Failed^{-1} +5 z^8 $Failed^{-1} -94 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-31 \text{QuantumGroups$\grave{ }$a}^5 z^7+\text{QuantumGroups$\grave{ }$a}^3 z^7+116 \text{QuantumGroups$\grave{ }$a} z^7+96 z^7 $Failed^{-1} -15 z^7 $Failed^{-1} -27 z^7 $Failed^{-1} +z^7 $Failed^{-1} -9 \text{QuantumGroups$\grave{ }$a}^6 z^6+47 \text{QuantumGroups$\grave{ }$a}^4 z^6+128 \text{QuantumGroups$\grave{ }$a}^2 z^6+113 z^6 $Failed^{-1} +24 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +150 z^6-2 \text{QuantumGroups$\grave{ }$a}^7 z^5+27 \text{QuantumGroups$\grave{ }$a}^5 z^5+24 \text{QuantumGroups$\grave{ }$a}^3 z^5-53 \text{QuantumGroups$\grave{ }$a} z^5-41 z^5 $Failed^{-1} +30 z^5 $Failed^{-1} +21 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^4-30 \text{QuantumGroups$\grave{ }$a}^4 z^4-82 \text{QuantumGroups$\grave{ }$a}^2 z^4-65 z^4 $Failed^{-1} -10 z^4 $Failed^{-1} +7 z^4 $Failed^{-1} -96 z^4+\text{QuantumGroups$\grave{ }$a}^7 z^3-16 \text{QuantumGroups$\grave{ }$a}^5 z^3-21 \text{QuantumGroups$\grave{ }$a}^3 z^3+17 \text{QuantumGroups$\grave{ }$a} z^3+19 z^3 $Failed^{-1} -11 z^3 $Failed^{-1} -8 z^3 $Failed^{-1} +z^3 $Failed^{-1} +12 \text{QuantumGroups$\grave{ }$a}^4 z^2+30 \text{QuantumGroups$\grave{ }$a}^2 z^2+19 z^2 $Failed^{-1} +4 z^2 $Failed^{-1} -z^2 $Failed^{-1} +32 z^2+5 \text{QuantumGroups$\grave{ }$a}^5 z+6 \text{QuantumGroups$\grave{ }$a}^3 z-3 \text{QuantumGroups$\grave{ }$a} z-7 z $Failed^{-1} -2 z $Failed^{-1} +z $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4-6 \text{QuantumGroups$\grave{ }$a}^2-2 $Failed^{-1} - $Failed^{-1} -3}

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