This page gives links to the output for Mochizuki's polynomial 3-cocycle knot invariants for Dihedral quandles. The Mochizuki polynomial 3-cocycle formula is f(x,y,z)=(x-y)[(2z^p-y^p)-(2z-y)^p]/p mod p. See section 2.6 in the background section for more information. Values for the invariant were calculated for the prime knots, their mirror images, with orientation reversed, and for some of the connected sums.
For prime knots.
Notes: R3 and R5 were calculated for prime knots in knotsLivingston.txt with 12 and fewer crossings. The valid color vectors were calculated with Maple. The values of the invariant for Rp where p ranges from 7 to 47 were calculated for prime knots with 9 and fewer crossings. The valid color vectors were calculated with a C program dynamically linked to Maple in these cases. All sections contain at least one non-trivial value.
| R3 | R5 | R7 |
| R11 | R13 | R17 |
| R19 | R23 | R29 |
| R31 | R37 | R41 |
| R43 | R47 |
Mirror images of prime knots.
Notes: The values of the invariant for Rp where p ranges from 3 to 47 were calculated for prime knots with 9 and fewer crossings. The braid words for the mirror images of the prime knots in knotsLivingston.txt were calculated with a Maple procedure. The valid color vectors were calculated with a C program dynamically linked to Maple in these cases. All sections contain at least one non-trivial value.
| R3 | R5 | R7 |
| R11 | R13 | R17 |
| R19 | R23 | R29 |
| R31 | R37 | R41 |
| R43 | R47 |
Prime knots with orientation reversed.
Notes: The values of the invariant for Rp where p ranges from 3 to 47 were calculated for prime knots with 9 and fewer crossings. The braid words for the prime knots in knotsLivingston.txt with their orientation reversed were calculated with a Maple procedure barKnot(). The valid color vectors were calculated with a C program dynamically linked to Maple in these cases. All sections contain at least one non-trivial value.
| R3 | R5 | R7 |
| R11 | R13 | R17 |
| R19 | R23 | R29 |
| R31 | R37 | R41 |
| R43 | R47 |
Connected sum of prime knots.
Notes: The values of the invariant for Rp where p ranges from 3 to 47 were calculated for prime knots with 9 and fewer crossings. The braid words for the connected sum of the prime knots in knotsLivingston.txt were calculated with a Maple procedure, connSumKnots(). The valid color vectors were calculated with a C program dynamically linked to Maple in these cases. All sections contain at least one non-trivial value.
| R3 | R5 |