K14a15224

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a15224

Polynomial invariants

Jones polynomial	Data:K14a15224/Jones Polynomial
Alexander polynomial	$t^{6}-4t^{5}+11t^{4}-22t^{3}+34t^{2}-42t+45-42t^{-1}+34t^{-2}-22t^{-3}+11t^{-4}-4t^{-5}+t^{-6}$
Conway polynomial	Data:K14a15224/Conway Polynomial
Determinant	Data:K14a15224/Determinant
Signature	Data:K14a15224/Signature
HOMFLY-PT polynomial	$a^{4}z^{12}-a^{6}z^{10}+10a^{4}z^{10}-a^{2}z^{10}-8a^{6}z^{8}+41a^{4}z^{8}-8a^{2}z^{8}-25a^{6}z^{6}+88a^{4}z^{6}-25a^{2}z^{6}-38a^{6}z^{4}+103a^{4}z^{4}-38a^{2}z^{4}-27a^{6}z^{2}+61a^{4}z^{2}-26a^{2}z^{2}-7a^{6}+13a^{4}-5a^{2}$
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}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-8 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+9 z^8 a^{10}-14 z^6 a^{10}+11 z^4 a^{10}-4 z^2 a^{10}+11 z^9 a^9-21 z^7 a^9+20 z^5 a^9-8 z^3 a^9+z a^9+11 z^{10} a^8-24 z^8 a^8+23 z^6 a^8-10 z^4 a^8+2 z^2 a^8+9 z^{11} a^7-21 z^9 a^7+20 z^7 a^7-15 z^5 a^7+8 z^3 a^7-2 z a^7+6 z^{12} a^6-15 z^{10} a^6+21 z^8 a^6-43 z^6 a^6+51 z^4 a^6-31 z^2 a^6+7 a^6+2 z^{13} a^5+5 z^{11} a^5-41 z^9 a^5+80 z^7 a^5-94 z^5 a^5+57 z^3 a^5-13 z a^5+11 z^{12} a^4-52 z^{10} a^4+109 z^8 a^4-159 z^6 a^4+146 z^4 a^4-71 z^2 a^4+13 a^4+2 z^{13} a^3+z^{11} a^3-35 z^9 a^3+79 z^7 a^3-88 z^5 a^3+53 z^3 a^3-11 z a^3+5 z^{12} a^2-23 z^{10} a^2+39 z^8 a^2-49 z^6 a^2+54 z^4 a^2-30 z^2 a^2+5 a^2+5 z^{11} a-25 z^9 a+40 z^7 a-26 z^5 a+9 z^3 a-z a+3 z^{10}-16 z^8+27 z^6-16 z^4+3 z^2+z^9 a^{-1} -6 z^7 a^{-1} +12 z^5 a^{-1} -9 z^3 a^{-1} +2 z a^{-1} }

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Large Knot Page master template. Back to the top.