K14a978

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a978

Polynomial invariants

Jones polynomial	Data:K14a978/Jones Polynomial
Alexander polynomial	$-2t^{4}+15t^{3}-47t^{2}+89t-109+89t^{-1}-47t^{-2}+15t^{-3}-2t^{-4}$
Conway polynomial	Data:K14a978/Conway Polynomial
Determinant	Data:K14a978/Determinant
Signature	Data:K14a978/Signature
HOMFLY-PT polynomial	$-z^{4}a^{8}-2z^{2}a^{8}-a^{8}+2z^{6}a^{6}+5z^{4}a^{6}+4z^{2}a^{6}-z^{8}a^{4}-2z^{6}a^{4}+4z^{2}a^{4}+3a^{4}-z^{8}a^{2}-3z^{6}a^{2}-6z^{4}a^{2}-7z^{2}a^{2}-3a^{2}+2z^{6}+6z^{4}+7z^{2}+3-z^{4}a^{-2}-2z^{2}a^{-2}-a^{-2}$
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{QuantumGroups$\grave{ }$a}^5 z^{13}+\text{QuantumGroups$\grave{ }$a}^3 z^{13}+5 \text{QuantumGroups$\grave{ }$a}^6 z^{12}+9 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+4 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+10 \text{QuantumGroups$\grave{ }$a}^7 z^{11}+21 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+18 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+7 \text{QuantumGroups$\grave{ }$a} z^{11}+11 \text{QuantumGroups$\grave{ }$a}^8 z^{10}+12 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+5 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+12 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+8 z^{10}+8 \text{QuantumGroups$\grave{ }$a}^9 z^9-14 \text{QuantumGroups$\grave{ }$a}^7 z^9-54 \text{QuantumGroups$\grave{ }$a}^5 z^9-39 \text{QuantumGroups$\grave{ }$a}^3 z^9+7 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^{10} z^8-24 \text{QuantumGroups$\grave{ }$a}^8 z^8-59 \text{QuantumGroups$\grave{ }$a}^6 z^8-60 \text{QuantumGroups$\grave{ }$a}^4 z^8-42 \text{QuantumGroups$\grave{ }$a}^2 z^8+4 z^8 $Failed^{-1} -9 z^8+\text{QuantumGroups$\grave{ }$a}^{11} z^7-19 \text{QuantumGroups$\grave{ }$a}^9 z^7-3 \text{QuantumGroups$\grave{ }$a}^7 z^7+48 \text{QuantumGroups$\grave{ }$a}^5 z^7+19 \text{QuantumGroups$\grave{ }$a}^3 z^7-29 \text{QuantumGroups$\grave{ }$a} z^7-16 z^7 $Failed^{-1} +z^7 $Failed^{-1} -11 \text{QuantumGroups$\grave{ }$a}^{10} z^6+17 \text{QuantumGroups$\grave{ }$a}^8 z^6+82 \text{QuantumGroups$\grave{ }$a}^6 z^6+92 \text{QuantumGroups$\grave{ }$a}^4 z^6+34 \text{QuantumGroups$\grave{ }$a}^2 z^6-12 z^6 $Failed^{-1} -16 z^6-3 \text{QuantumGroups$\grave{ }$a}^{11} z^5+12 \text{QuantumGroups$\grave{ }$a}^9 z^5+10 \text{QuantumGroups$\grave{ }$a}^7 z^5-6 \text{QuantumGroups$\grave{ }$a}^5 z^5+20 \text{QuantumGroups$\grave{ }$a}^3 z^5+32 \text{QuantumGroups$\grave{ }$a} z^5+8 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^{10} z^4-12 \text{QuantumGroups$\grave{ }$a}^8 z^4-54 \text{QuantumGroups$\grave{ }$a}^6 z^4-46 \text{QuantumGroups$\grave{ }$a}^4 z^4+\text{QuantumGroups$\grave{ }$a}^2 z^4+12 z^4 $Failed^{-1} +26 z^4+3 \text{QuantumGroups$\grave{ }$a}^{11} z^3-3 \text{QuantumGroups$\grave{ }$a}^9 z^3-9 \text{QuantumGroups$\grave{ }$a}^7 z^3-9 \text{QuantumGroups$\grave{ }$a}^5 z^3-18 \text{QuantumGroups$\grave{ }$a}^3 z^3-14 \text{QuantumGroups$\grave{ }$a} z^3+z^3 $Failed^{-1} +3 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^{10} z^2+6 \text{QuantumGroups$\grave{ }$a}^8 z^2+13 \text{QuantumGroups$\grave{ }$a}^6 z^2+3 \text{QuantumGroups$\grave{ }$a}^4 z^2-11 \text{QuantumGroups$\grave{ }$a}^2 z^2-5 z^2 $Failed^{-1} -14 z^2-\text{QuantumGroups$\grave{ }$a}^{11} z+\text{QuantumGroups$\grave{ }$a}^9 z+2 \text{QuantumGroups$\grave{ }$a}^7 z+2 \text{QuantumGroups$\grave{ }$a}^5 z+4 \text{QuantumGroups$\grave{ }$a}^3 z+2 \text{QuantumGroups$\grave{ }$a} z-z $Failed^{-1} -z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8+3 \text{QuantumGroups$\grave{ }$a}^4+3 \text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} +3}

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