K13a2020

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a2020

Polynomial invariants

Jones polynomial	Data:K13a2020/Jones Polynomial
Alexander polynomial	$-2t^{4}+13t^{3}-40t^{2}+74t-89+74t^{-1}-40t^{-2}+13t^{-3}-2t^{-4}$
Conway polynomial	Data:K13a2020/Conway Polynomial
Determinant	347
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-2}-z^{8}+a^{2}z^{6}-2z^{6}a^{-2}+2z^{6}a^{-4}-4z^{6}+3a^{2}z^{4}+4z^{4}a^{-4}-z^{4}a^{-6}-8z^{4}+3a^{2}z^{2}+2z^{2}a^{-2}+2z^{2}a^{-4}-z^{2}a^{-6}-7z^{2}+a^{2}+a^{-2}-1$
Kauffman polynomial	$2z^{12}a^{-2}+2z^{12}+6az^{11}+16z^{11}a^{-1}+10z^{11}a^{-3}+7a^{2}z^{10}+35z^{10}a^{-2}+22z^{10}a^{-4}+20z^{10}+4a^{3}z^{9}-6az^{9}-15z^{9}a^{-1}+23z^{9}a^{-3}+28z^{9}a^{-5}+a^{4}z^{8}-24a^{2}z^{8}-97z^{8}a^{-2}-20z^{8}a^{-4}+23z^{8}a^{-6}-79z^{8}-16a^{3}z^{7}-30az^{7}-61z^{7}a^{-1}-104z^{7}a^{-3}-44z^{7}a^{-5}+13z^{7}a^{-7}-4a^{4}z^{6}+27a^{2}z^{6}+69z^{6}a^{-2}-26z^{6}a^{-4}-31z^{6}a^{-6}+5z^{6}a^{-8}+90z^{6}+22a^{3}z^{5}+58az^{5}+99z^{5}a^{-1}+98z^{5}a^{-3}+23z^{5}a^{-5}-11z^{5}a^{-7}+z^{5}a^{-9}+5a^{4}z^{4}-12a^{2}z^{4}-15z^{4}a^{-2}+29z^{4}a^{-4}+16z^{4}a^{-6}-2z^{4}a^{-8}-43z^{4}-12a^{3}z^{3}-34az^{3}-50z^{3}a^{-1}-37z^{3}a^{-3}-6z^{3}a^{-5}+3z^{3}a^{-7}-2a^{4}z^{2}+3a^{2}z^{2}+2z^{2}a^{-2}-7z^{2}a^{-4}-3z^{2}a^{-6}+11z^{2}+2a^{3}z+6az+8za^{-1}+5za^{-3}+za^{-5}-a^{2}-a^{-2}-1$

Modifying This Page

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