K12n242

Knotscape

Pretzel

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12n242

Polynomial invariants

Jones polynomial	$-q^{13}+q^{12}-q^{11}+q^{7}+q^{5}$
Alexander polynomial	$t^{5}-t^{4}+t^{2}-t+1-t^{-1}+t^{-2}-t^{-4}+t^{-5}$
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}+9 z^8+27 z^6+31 z^4+12 z^2+1}
Determinant	1
Signature	8
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^{10} a^{-10} +10 z^8 a^{-10} -z^8 a^{-12} +36 z^6 a^{-10} -9 z^6 a^{-12} +57 z^4 a^{-10} -27 z^4 a^{-12} +z^4 a^{-14} +39 z^2 a^{-10} -31 z^2 a^{-12} +4 z^2 a^{-14} +9 a^{-10} -11 a^{-12} +3 a^{-14} }
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^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-11} +z^9 a^{-13} -10 z^8 a^{-10} -10 z^8 a^{-12} -9 z^7 a^{-11} -9 z^7 a^{-13} +36 z^6 a^{-10} +36 z^6 a^{-12} +27 z^5 a^{-11} +27 z^5 a^{-13} -57 z^4 a^{-10} -58 z^4 a^{-12} -z^4 a^{-14} -31 z^3 a^{-11} -31 z^3 a^{-13} +39 z^2 a^{-10} +42 z^2 a^{-12} +4 z^2 a^{-14} +z^2 a^{-16} +11 z a^{-11} +11 z a^{-13} +z a^{-15} +z a^{-17} -9 a^{-10} -11 a^{-12} -3 a^{-14} }

Modifying This Page

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