K12a1002

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1002

Polynomial invariants

Jones 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 -q^4+4 q^3-9 q^2+15 q-21+27 q^{-1} -28 q^{-2} +27 q^{-3} -22 q^{-4} +15 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }
Alexander polynomial	$t^{5}-5t^{4}+13t^{3}-23t^{2}+32t-35+32t^{-1}-23t^{-2}+13t^{-3}-5t^{-4}+t^{-5}$
Conway 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 z^{10}+5 z^8+8 z^6+5 z^4+2 z^2+1}
Determinant	183
Signature	-2
HOMFLY-PT 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 a^2 z^{10}-a^4 z^8+7 a^2 z^8-z^8-5 a^4 z^6+18 a^2 z^6-5 z^6-8 a^4 z^4+21 a^2 z^4-8 z^4-5 a^4 z^2+12 a^2 z^2-5 z^2-2 a^4+4 a^2-1}
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 3 a^3 z^{11}+3 a z^{11}+8 a^4 z^{10}+15 a^2 z^{10}+7 z^{10}+11 a^5 z^9+7 a^3 z^9+3 a z^9+7 z^9 a^{-1} +11 a^6 z^8-13 a^4 z^8-49 a^2 z^8+4 z^8 a^{-2} -21 z^8+8 a^7 z^7-21 a^5 z^7-36 a^3 z^7-31 a z^7-23 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-20 a^6 z^6+6 a^4 z^6+64 a^2 z^6-13 z^6 a^{-2} +21 z^6+a^9 z^5-12 a^7 z^5+16 a^5 z^5+47 a^3 z^5+42 a z^5+21 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+14 a^6 z^4+2 a^4 z^4-43 a^2 z^4+10 z^4 a^{-2} -16 z^4-a^9 z^3+4 a^7 z^3-3 a^5 z^3-23 a^3 z^3-25 a z^3-8 z^3 a^{-1} +2 z^3 a^{-3} -4 a^6 z^2+3 a^4 z^2+15 a^2 z^2-z^2 a^{-2} +7 z^2-a^7 z+a^5 z+5 a^3 z+5 a z+2 z a^{-1} -2 a^4-4 a^2-1}

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