Notice. The Knot Atlas is now recovering from a major crash. Hopefully all functionality will return slowly over the next few days. --Drorbn (talk) 21:23, 4 July 2013 (EDT)

K12n242

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Contents

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



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