K12n242

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

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