% $Date: 2003/09/15 16:37:45 $ $Author: nthiery $ $Revision: 1.1.1.1 $

\begin{Mhelppage}{Part2PCore}{V. Prosper}%
  \begin{MInfo}
    \eng{\Mex{p}-core and \Mex{p}-quotient of a partition}
  \end{MInfo}

\begin{MCalls}
  \Mcall{part,p}
\end{MCalls}

\begin{MParameters}
  \param{part}
  \eng{a partition} 
  \param{p}
  \eng{an integer} 
\end{MParameters}

\begin{MIntro}
  \eng{
To a partition \Mex{part} and an integer \Mex{p}, the function {\Mthis}
associates a list
\Mmath{[c, v0, v1, ..., v\{\Mex{p}-1\}]}{[c, v_0, v_1, ..., v_{\mathtt{p}-1}]}:
\Mmath{c}{c}  is the \Mex{p}-core  (obtained by removing all  possible outside
ribbons of length \Mex{p} from the diagram of \Mex{part});
\Mmath{v0, v1, ..., v\{p-1\}}{v_0, v_1, ..., v_{\mathtt{p}-1}} are the
partitions obtained from the residues modulo \Mex{p} of
\Mex{part}[1], \Mex{part}[2]-1, \Mex{part}[3]-2, ...
}
\end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::PART::Part2PCore( [5,5,5,4,3,3,2,1,1,1], 3 );
\end{Mexin}
\begin{Mexout}
            [[2, 2, 1, 1], [1, 1, 1], [1], [3, 1]]
\end{Mexout}
\end{MExample}

\MRelatedFunctions{PCore2Part}
\end{Mhelppage}
