K13n321

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13n321

Polynomial invariants

Jones polynomial	Data:K13n321/Jones Polynomial
Alexander polynomial	$-4t^{3}+20t^{2}-42t+53-42t^{-1}+20t^{-2}-4t^{-3}$
Conway polynomial	Data:K13n321/Conway Polynomial
Determinant	185
Signature	4
HOMFLY-PT polynomial	$-z^{6}a^{-4}-3z^{6}a^{-6}+z^{4}a^{-2}-10z^{4}a^{-6}+5z^{4}a^{-8}+2z^{2}a^{-2}+4z^{2}a^{-4}-13z^{2}a^{-6}+11z^{2}a^{-8}-2z^{2}a^{-10}+a^{-2}+3a^{-4}-7a^{-6}+6a^{-8}-2a^{-10}$
Kauffman polynomial	$z^{11}a^{-7}+z^{11}a^{-9}+4z^{10}a^{-6}+7z^{10}a^{-8}+3z^{10}a^{-10}+7z^{9}a^{-5}+15z^{9}a^{-7}+11z^{9}a^{-9}+3z^{9}a^{-11}+6z^{8}a^{-4}+10z^{8}a^{-6}+8z^{8}a^{-8}+5z^{8}a^{-10}+z^{8}a^{-12}+3z^{7}a^{-3}-9z^{7}a^{-5}-26z^{7}a^{-7}-11z^{7}a^{-9}+3z^{7}a^{-11}+z^{6}a^{-2}-12z^{6}a^{-4}-41z^{6}a^{-6}-42z^{6}a^{-8}-8z^{6}a^{-10}+6z^{6}a^{-12}-6z^{5}a^{-3}+z^{5}a^{-5}+5z^{5}a^{-7}-12z^{5}a^{-9}-7z^{5}a^{-11}+3z^{5}a^{-13}-3z^{4}a^{-2}+11z^{4}a^{-4}+50z^{4}a^{-6}+45z^{4}a^{-8}-2z^{4}a^{-10}-11z^{4}a^{-12}+3z^{3}a^{-3}+3z^{3}a^{-5}+10z^{3}a^{-7}+16z^{3}a^{-9}+2z^{3}a^{-11}-4z^{3}a^{-13}+3z^{2}a^{-2}-8z^{2}a^{-4}-30z^{2}a^{-6}-24z^{2}a^{-8}+5z^{2}a^{-12}-2za^{-5}-5za^{-7}-5za^{-9}-za^{-11}+za^{-13}-a^{-2}+3a^{-4}+7a^{-6}+6a^{-8}+2a^{-10}$

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