FUNCTION: Part2PCore - p-core and p-quotient of a partition

CALLING SEQUENCE:

Part2PCore(part, p)

PART[Part2PCore](part, p)

PARAMETERS:

part = a partition

p = an integer

SYNOPSIS:

• To a partition part and an integer p, the function Part2PCore associates a list [c, v0, v1, ..., v{p-1}]: c is the p-core (obtained by removing all possible outside ribbons of length p from the diagram of part; v0, v1, ..., v{p-1} are the partitions obtained by sorting part[1] part[2]-1, part[3]-2, ..., according to their classes modulo p.

• Whenever there is a conflict between the function name Part2PCore and another name used in the same session, use the long form PART['Part2PCore'].

EXAMPLES:

> with(PART):
> Part2PCore([5,5,5,4,3,3,2,1,1,1],3);
 
                     [[2, 2, 1, 1], [1, 1, 1], [1], [3, 1]]