K13n3246

From Knot Atlas
Jump to navigationJump to search

Polynomial invariants

Jones polynomial Data:K13n3246/Jones Polynomial
Alexander polynomial [math]\displaystyle{ -2 t^3+8 t^2-18 t+25-18 t^{-1} +8 t^{-2} -2 t^{-3} }[/math]
Conway polynomial Data:K13n3246/Conway Polynomial
Determinant 81
Signature 0
HOMFLY-PT polynomial [math]\displaystyle{ -a^2 z^6-z^6+a^4 z^4-3 a^2 z^4+z^4 a^{-2} -3 z^4+2 a^4 z^2-3 a^2 z^2+z^2 a^{-2} -4 z^2+a^4+ a^{-4} -1 }[/math]
Kauffman polynomial [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+z^{10} a^{-2} +4 z^{10}+4 a^3 z^9-4 z^9 a^{-1} +4 a^4 z^8-10 a^2 z^8-5 z^8 a^{-2} -19 z^8+3 a^5 z^7-12 a^3 z^7-10 a z^7+6 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-11 a^4 z^6+13 a^2 z^6+12 z^6 a^{-2} +37 z^6-9 a^5 z^5+12 a^3 z^5+23 a z^5+2 z^5 a^{-1} -3 a^6 z^4+6 a^4 z^4-6 a^2 z^4-9 z^4 a^{-2} +2 z^4 a^{-4} -26 z^4+5 a^5 z^3-9 a^3 z^3-13 a z^3-3 z^3 a^{-1} -4 z^3 a^{-3} +2 a^6 z^2-3 a^4 z^2-a^2 z^2+z^2 a^{-2} -5 z^2 a^{-4} +10 z^2+2 a^3 z+2 a z+2 z a^{-1} +2 z a^{-3} +a^4+ a^{-4} -1 }[/math]



Modifying This Page

Read me first: Modifying Knot Pages

See/edit the Large Knot Page master template.

Back to the top.