K13a4304

Knotscape

Decorative quasi-Celtic knot

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a4304

Polynomial invariants

Jones polynomial	Data:K13a4304/Jones Polynomial
Alexander polynomial	[math]\displaystyle{ 16 t^2-52 t+73-52 t^{-1} +16 t^{-2} }[/math]
Conway polynomial	Data:K13a4304/Conway Polynomial
Determinant	209
Signature	4
HOMFLY-PT polynomial	[math]\displaystyle{ z^4 a^{-4} +4 z^4 a^{-6} +6 z^4 a^{-8} +4 z^4 a^{-10} +z^4 a^{-12} +4 z^2 a^{-6} +8 z^2 a^{-8} +3 z^2 a^{-10} -2 z^2 a^{-12} -z^2 a^{-14} +3 a^{-8} -2 a^{-12} }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{12} a^{-12} +z^{12} a^{-14} +4 z^{11} a^{-11} +7 z^{11} a^{-13} +3 z^{11} a^{-15} +10 z^{10} a^{-10} +13 z^{10} a^{-12} +6 z^{10} a^{-14} +3 z^{10} a^{-16} +16 z^9 a^{-9} +13 z^9 a^{-11} -15 z^9 a^{-13} -11 z^9 a^{-15} +z^9 a^{-17} +19 z^8 a^{-8} -5 z^8 a^{-10} -48 z^8 a^{-12} -41 z^8 a^{-14} -17 z^8 a^{-16} +16 z^7 a^{-7} -23 z^7 a^{-9} -71 z^7 a^{-11} -23 z^7 a^{-13} +3 z^7 a^{-15} -6 z^7 a^{-17} +10 z^6 a^{-6} -32 z^6 a^{-8} -37 z^6 a^{-10} +34 z^6 a^{-12} +62 z^6 a^{-14} +33 z^6 a^{-16} +4 z^5 a^{-5} -20 z^5 a^{-7} -2 z^5 a^{-9} +76 z^5 a^{-11} +66 z^5 a^{-13} +25 z^5 a^{-15} +13 z^5 a^{-17} +z^4 a^{-4} -8 z^4 a^{-6} +21 z^4 a^{-8} +32 z^4 a^{-10} +2 z^4 a^{-12} -24 z^4 a^{-14} -24 z^4 a^{-16} +8 z^3 a^{-7} -34 z^3 a^{-11} -38 z^3 a^{-13} -24 z^3 a^{-15} -12 z^3 a^{-17} +4 z^2 a^{-6} -14 z^2 a^{-8} -9 z^2 a^{-10} +4 z^2 a^{-12} -z^2 a^{-14} +4 z^2 a^{-16} +8 z a^{-11} +8 z a^{-13} +4 z a^{-15} +4 z a^{-17} +3 a^{-8} -2 a^{-12} }[/math]

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