K12a607

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a607

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+4-9 q^{-1} +16 q^{-2} -21 q^{-3} +26 q^{-4} -27 q^{-5} +25 q^{-6} -20 q^{-7} +13 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }
Alexander polynomial	$2t^{4}-9t^{3}+22t^{2}-34t+39-34t^{-1}+22t^{-2}-9t^{-3}+2t^{-4}$
Conway polynomial	$2z^{8}+7z^{6}+8z^{4}+5z^{2}+1$
Determinant	173
Signature	-4
HOMFLY-PT polynomial	$-z^{6}a^{8}-4z^{4}a^{8}-5z^{2}a^{8}-2a^{8}+z^{8}a^{6}+5z^{6}a^{6}+10z^{4}a^{6}+9z^{2}a^{6}+2a^{6}+z^{8}a^{4}+4z^{6}a^{4}+5z^{4}a^{4}+3z^{2}a^{4}+a^{4}-z^{6}a^{2}-3z^{4}a^{2}-2z^{2}a^{2}$
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 z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-5 z^4 a^{12}+2 z^2 a^{12}+5 z^7 a^{11}-6 z^5 a^{11}+z^3 a^{11}+7 z^8 a^{10}-10 z^6 a^{10}+7 z^4 a^{10}-3 z^2 a^{10}+8 z^9 a^9-15 z^7 a^9+17 z^5 a^9-9 z^3 a^9+2 z a^9+6 z^{10} a^8-7 z^8 a^8-z^6 a^8+6 z^4 a^8+2 z^2 a^8-2 a^8+2 z^{11} a^7+11 z^9 a^7-43 z^7 a^7+52 z^5 a^7-24 z^3 a^7+4 z a^7+12 z^{10} a^6-30 z^8 a^6+21 z^6 a^6-7 z^4 a^6+6 z^2 a^6-2 a^6+2 z^{11} a^5+10 z^9 a^5-46 z^7 a^5+50 z^5 a^5-21 z^3 a^5+2 z a^5+6 z^{10} a^4-12 z^8 a^4-4 z^6 a^4+11 z^4 a^4-5 z^2 a^4+a^4+7 z^9 a^3-22 z^7 a^3+19 z^5 a^3-7 z^3 a^3+z a^3+4 z^8 a^2-13 z^6 a^2+12 z^4 a^2-4 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a}

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