K13a4532

Knotscape

Angular decorative knot

Angular decorative knot with central pentagram

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a4532

Polynomial invariants

Jones polynomial	Data:K13a4532/Jones Polynomial
Alexander polynomial	$4t^{3}-16t^{2}+25t-25+25t^{-1}-16t^{-2}+4t^{-3}$
Conway polynomial	Data:K13a4532/Conway Polynomial
Determinant	115
Signature	2
HOMFLY-PT polynomial	$z^{2}a^{6}+2a^{6}-2z^{4}a^{4}-6z^{2}a^{4}-3a^{4}+z^{6}a^{2}+2z^{4}a^{2}-z^{2}a^{2}+2z^{6}+7z^{4}+6z^{2}+2+z^{6}a^{-2}+2z^{4}a^{-2}-z^{2}a^{-2}-z^{4}a^{-4}-2z^{2}a^{-4}$
Kauffman polynomial	$a^{4}z^{12}+a^{2}z^{12}+2a^{5}z^{11}+5a^{3}z^{11}+3az^{11}+a^{6}z^{10}-3a^{4}z^{10}+2a^{2}z^{10}+6z^{10}-15a^{5}z^{9}-29a^{3}z^{9}-4az^{9}+10z^{9}a^{-1}-8a^{6}z^{8}-10a^{4}z^{8}-28a^{2}z^{8}+12z^{8}a^{-2}-14z^{8}+40a^{5}z^{7}+54a^{3}z^{7}-28az^{7}-30z^{7}a^{-1}+12z^{7}a^{-3}+23a^{6}z^{6}+47a^{4}z^{6}+50a^{2}z^{6}-30z^{6}a^{-2}+10z^{6}a^{-4}-14z^{6}-45a^{5}z^{5}-35a^{3}z^{5}+62az^{5}+22z^{5}a^{-1}-24z^{5}a^{-3}+6z^{5}a^{-5}-28a^{6}z^{4}-57a^{4}z^{4}-22a^{2}z^{4}+15z^{4}a^{-2}-15z^{4}a^{-4}+3z^{4}a^{-6}+40z^{4}+20a^{5}z^{3}+6a^{3}z^{3}-38az^{3}-11z^{3}a^{-1}+9z^{3}a^{-3}-3z^{3}a^{-5}+z^{3}a^{-7}+13a^{6}z^{2}+25a^{4}z^{2}+a^{2}z^{2}-3z^{2}a^{-2}+6z^{2}a^{-4}-20z^{2}-3a^{5}z+a^{3}z+8az+4za^{-1}-2a^{6}-3a^{4}+2$

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