# K13a4878

K13a4878 is the next knot in the sequence trefoil, cinquefoil, septafoil, nonafoil, K11a367...

Interlaced form of 13/2 star polygon
Decorative interlaced form of 13/2 star polygon

## Contents

### Knot presentations

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

### Polynomial invariants

 Jones polynomial Data:K13a4878/Jones Polynomial Alexander polynomial $t^6-t^5+t^4-t^3+t^2-t+1- t^{-1} + t^{-2} - t^{-3} + t^{-4} - t^{-5} + t^{-6}$ Conway polynomial Data:K13a4878/Conway Polynomial Determinant 13 Signature 12 HOMFLY-PT polynomial $z^{12} a^{-12} +12 z^{10} a^{-12} -z^{10} a^{-14} +55 z^8 a^{-12} -10 z^8 a^{-14} +120 z^6 a^{-12} -36 z^6 a^{-14} +126 z^4 a^{-12} -56 z^4 a^{-14} +56 z^2 a^{-12} -35 z^2 a^{-14} +7 a^{-12} -6 a^{-14}$ Kauffman polynomial $z^{12} a^{-12} +z^{12} a^{-14} +z^{11} a^{-13} +z^{11} a^{-15} -12 z^{10} a^{-12} -11 z^{10} a^{-14} +z^{10} a^{-16} -10 z^9 a^{-13} -9 z^9 a^{-15} +z^9 a^{-17} +55 z^8 a^{-12} +46 z^8 a^{-14} -8 z^8 a^{-16} +z^8 a^{-18} +36 z^7 a^{-13} +28 z^7 a^{-15} -7 z^7 a^{-17} +z^7 a^{-19} -120 z^6 a^{-12} -92 z^6 a^{-14} +21 z^6 a^{-16} -6 z^6 a^{-18} +z^6 a^{-20} -56 z^5 a^{-13} -35 z^5 a^{-15} +15 z^5 a^{-17} -5 z^5 a^{-19} +z^5 a^{-21} +126 z^4 a^{-12} +91 z^4 a^{-14} -20 z^4 a^{-16} +10 z^4 a^{-18} -4 z^4 a^{-20} +z^4 a^{-22} +35 z^3 a^{-13} +15 z^3 a^{-15} -10 z^3 a^{-17} +6 z^3 a^{-19} -3 z^3 a^{-21} +z^3 a^{-23} -56 z^2 a^{-12} -41 z^2 a^{-14} +5 z^2 a^{-16} -4 z^2 a^{-18} +3 z^2 a^{-20} -2 z^2 a^{-22} +z^2 a^{-24} -6 z a^{-13} -z a^{-15} +z a^{-17} -z a^{-19} +z a^{-21} -z a^{-23} +z a^{-25} +7 a^{-12} +6 a^{-14}$