K13n2811

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13n2811

Polynomial invariants

Jones polynomial	Data:K13n2811/Jones Polynomial
Alexander polynomial	$-t^{5}+5t^{4}-11t^{3}+16t^{2}-17t+17-17t^{-1}+16t^{-2}-11t^{-3}+5t^{-4}-t^{-5}$
Conway polynomial	Data:K13n2811/Conway Polynomial
Determinant	117
Signature	4
HOMFLY-PT polynomial	$-z^{10}a^{-4}+z^{8}a^{-2}-7z^{8}a^{-4}+z^{8}a^{-6}+5z^{6}a^{-2}-17z^{6}a^{-4}+6z^{6}a^{-6}+7z^{4}a^{-2}-16z^{4}a^{-4}+10z^{4}a^{-6}-z^{4}a^{-8}+2z^{2}a^{-2}+2z^{2}a^{-6}-z^{2}a^{-8}-a^{-2}+6a^{-4}-5a^{-6}+a^{-8}$
Kauffman polynomial	$3z^{11}a^{-3}+3z^{11}a^{-5}+6z^{10}a^{-2}+14z^{10}a^{-4}+8z^{10}a^{-6}+4z^{9}a^{-1}-3z^{9}a^{-3}+z^{9}a^{-5}+8z^{9}a^{-7}-27z^{8}a^{-2}-62z^{8}a^{-4}-31z^{8}a^{-6}+3z^{8}a^{-8}+z^{8}-18z^{7}a^{-1}-28z^{7}a^{-3}-43z^{7}a^{-5}-33z^{7}a^{-7}+38z^{6}a^{-2}+83z^{6}a^{-4}+31z^{6}a^{-6}-10z^{6}a^{-8}-4z^{6}+24z^{5}a^{-1}+48z^{5}a^{-3}+61z^{5}a^{-5}+38z^{5}a^{-7}+z^{5}a^{-9}-24z^{4}a^{-2}-46z^{4}a^{-4}-7z^{4}a^{-6}+11z^{4}a^{-8}+4z^{4}-10z^{3}a^{-1}-22z^{3}a^{-3}-17z^{3}a^{-5}-4z^{3}a^{-7}+z^{3}a^{-9}+5z^{2}a^{-2}+4z^{2}a^{-4}-3z^{2}a^{-6}-2z^{2}a^{-8}-za^{-3}-7za^{-5}-8za^{-7}-2za^{-9}+a^{-2}+6a^{-4}+5a^{-6}+a^{-8}$

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