K13a1814

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Knotscape
Symmetrical depiction as decorative knot
More squared symmetrical depiction.


Contents

Knot presentations

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

Notes on presentations of K13a1814

Polynomial invariants

Jones polynomial Data:K13a1814/Jones Polynomial
Alexander polynomial -t^4+9 t^3-33 t^2+67 t-83+67 t^{-1} -33 t^{-2} +9 t^{-3} - t^{-4}
Conway polynomial Data:K13a1814/Conway Polynomial
Determinant 303
Signature 2
HOMFLY-PT polynomial -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +3 z^6-3 a^2 z^4-9 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +9 z^4+a^4 z^2-6 a^2 z^2-8 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +10 z^2+a^4-3 a^2- a^{-2} +4
Kauffman polynomial z^{12} a^{-2} +z^{12}+4 a z^{11}+9 z^{11} a^{-1} +5 z^{11} a^{-3} +6 a^2 z^{10}+24 z^{10} a^{-2} +12 z^{10} a^{-4} +18 z^{10}+4 a^3 z^9+5 a z^9+12 z^9 a^{-1} +29 z^9 a^{-3} +18 z^9 a^{-5} +a^4 z^8-17 a^2 z^8-41 z^8 a^{-2} +11 z^8 a^{-4} +18 z^8 a^{-6} -52 z^8-16 a^3 z^7-56 a z^7-100 z^7 a^{-1} -87 z^7 a^{-3} -15 z^7 a^{-5} +12 z^7 a^{-7} -4 a^4 z^6+6 a^2 z^6-30 z^6 a^{-2} -64 z^6 a^{-4} -23 z^6 a^{-6} +5 z^6 a^{-8} +16 z^6+23 a^3 z^5+85 a z^5+120 z^5 a^{-1} +63 z^5 a^{-3} -9 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +6 a^4 z^4+18 a^2 z^4+68 z^4 a^{-2} +53 z^4 a^{-4} +12 z^4 a^{-6} -3 z^4 a^{-8} +42 z^4-14 a^3 z^3-45 a z^3-50 z^3 a^{-1} -18 z^3 a^{-3} +6 z^3 a^{-5} +5 z^3 a^{-7} -4 a^4 z^2-16 a^2 z^2-27 z^2 a^{-2} -15 z^2 a^{-4} -4 z^2 a^{-6} -28 z^2+3 a^3 z+8 a z+8 z a^{-1} +4 z a^{-3} +z a^{-5} +a^4+3 a^2+ a^{-2} +4



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