K14a13842

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13842

Polynomial invariants

Jones polynomial	Data:K14a13842/Jones Polynomial
Alexander polynomial	$t^{5}-8t^{4}+32t^{3}-77t^{2}+126t-147+126t^{-1}-77t^{-2}+32t^{-3}-8t^{-4}+t^{-5}$
Conway polynomial	Data:K14a13842/Conway Polynomial
Determinant	Data:K14a13842/Determinant
Signature	Data:K14a13842/Signature
HOMFLY-PT polynomial	$z^{10}a^{-2}+6z^{8}a^{-2}-3z^{8}a^{-4}-z^{8}+18z^{6}a^{-2}-14z^{6}a^{-4}+3z^{6}a^{-6}-4z^{6}+30z^{4}a^{-2}-27z^{4}a^{-4}+11z^{4}a^{-6}-z^{4}a^{-8}-8z^{4}+25z^{2}a^{-2}-25z^{2}a^{-4}+14z^{2}a^{-6}-3z^{2}a^{-8}-8z^{2}+8a^{-2}-9a^{-4}+6a^{-6}-2a^{-8}-2$
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 4 z^{13} $Failed^{-1} +4 z^{13} $Failed^{-1} +16 z^{12} $Failed^{-1} +29 z^{12} $Failed^{-1} +13 z^{12} $Failed^{-1} +27 z^{11} $Failed^{-1} +49 z^{11} $Failed^{-1} +40 z^{11} $Failed^{-1} +18 z^{11} $Failed^{-1} +9 z^{10} $Failed^{-1} -31 z^{10} $Failed^{-1} +15 z^{10} $Failed^{-1} +25 z^{10}+14 \text{QuantumGroups$\grave{ }$a} z^9-52 z^9 $Failed^{-1} -154 z^9 $Failed^{-1} -132 z^9 $Failed^{-1} -35 z^9 $Failed^{-1} +9 z^9 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^2 z^8-111 z^8 $Failed^{-1} -70 z^8 $Failed^{-1} -59 z^8 $Failed^{-1} -32 z^8 $Failed^{-1} +4 z^8 $Failed^{-1} -59 z^8+\text{QuantumGroups$\grave{ }$a}^3 z^7-29 \text{QuantumGroups$\grave{ }$a} z^7+28 z^7 $Failed^{-1} +178 z^7 $Failed^{-1} +174 z^7 $Failed^{-1} +34 z^7 $Failed^{-1} -19 z^7 $Failed^{-1} +z^7 $Failed^{-1} -9 \text{QuantumGroups$\grave{ }$a}^2 z^6+176 z^6 $Failed^{-1} +178 z^6 $Failed^{-1} +113 z^6 $Failed^{-1} +31 z^6 $Failed^{-1} -10 z^6 $Failed^{-1} +61 z^6-2 \text{QuantumGroups$\grave{ }$a}^3 z^5+22 \text{QuantumGroups$\grave{ }$a} z^5-z^5 $Failed^{-1} -100 z^5 $Failed^{-1} -113 z^5 $Failed^{-1} -23 z^5 $Failed^{-1} +12 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^2 z^4-140 z^4 $Failed^{-1} -157 z^4 $Failed^{-1} -98 z^4 $Failed^{-1} -23 z^4 $Failed^{-1} +8 z^4 $Failed^{-1} -46 z^4+\text{QuantumGroups$\grave{ }$a}^3 z^3-10 \text{QuantumGroups$\grave{ }$a} z^3-9 z^3 $Failed^{-1} +24 z^3 $Failed^{-1} +35 z^3 $Failed^{-1} +8 z^3 $Failed^{-1} -2 z^3 $Failed^{-1} +3 z^3 $Failed^{-1} +55 z^2 $Failed^{-1} +63 z^2 $Failed^{-1} +40 z^2 $Failed^{-1} +11 z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +19 z^2+2 \text{QuantumGroups$\grave{ }$a} z+3 z $Failed^{-1} -z $Failed^{-1} -4 z $Failed^{-1} -z $Failed^{-1} -z $Failed^{-1} -8 $Failed^{-1} -9 $Failed^{-1} -6 $Failed^{-1} -2 $Failed^{-1} -2}

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