K12a1109

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1109

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^9-5 q^8+12 q^7-22 q^6+31 q^5-37 q^4+40 q^3-36 q^2+29 q-19+10 q^{-1} -4 q^{-2} + q^{-3} }
Alexander polynomial	$-2t^{4}+11t^{3}-29t^{2}+51t-61+51t^{-1}-29t^{-2}+11t^{-3}-2t^{-4}$
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 -2 z^8-5 z^6-3 z^4+2 z^2+1}
Determinant	247
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 -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-7 z^4 a^{-2} -z^4 a^{-4} +2 z^4 a^{-6} +3 z^4-6 z^2 a^{-2} +5 z^2 a^{-4} +3 z^2-2 a^{-2} +4 a^{-4} -2 a^{-6} +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 4 z^{11} a^{-3} +4 z^{11} a^{-5} +10 z^{10} a^{-2} +22 z^{10} a^{-4} +12 z^{10} a^{-6} +11 z^9 a^{-1} +15 z^9 a^{-3} +19 z^9 a^{-5} +15 z^9 a^{-7} -13 z^8 a^{-2} -48 z^8 a^{-4} -16 z^8 a^{-6} +11 z^8 a^{-8} +8 z^8+4 a z^7-20 z^7 a^{-1} -56 z^7 a^{-3} -67 z^7 a^{-5} -30 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-3 z^6 a^{-2} +33 z^6 a^{-4} -z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -15 z^6-8 a z^5+11 z^5 a^{-1} +64 z^5 a^{-3} +73 z^5 a^{-5} +20 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+17 z^4 a^{-2} +5 z^4 a^{-4} +7 z^4 a^{-6} +8 z^4 a^{-8} -z^4 a^{-10} +8 z^4+4 a z^3-2 z^3 a^{-1} -24 z^3 a^{-3} -30 z^3 a^{-5} -10 z^3 a^{-7} +2 z^3 a^{-9} +a^2 z^2-11 z^2 a^{-2} -11 z^2 a^{-4} -6 z^2 a^{-6} -z^2 a^{-8} -4 z^2-a z-z a^{-1} +2 z a^{-3} +2 z a^{-5} +z a^{-7} +z a^{-9} +2 a^{-2} +4 a^{-4} +2 a^{-6} +1}

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