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

\begin{Mhelppage}{ListPartIn}{V. Prosper}%
  \begin{MInfo}
    \eng{list of partitions contained into a given partition or
      between two given partitions}
  \end{MInfo}

  \MDeclareOption{\weight}{weight}
  \MDeclareOption{\nb}{nb}

  \begin{MCalls}
    \Mcall{part\Mopt{,partin}\Mopt{,options}}
  \end{MCalls}

  \begin{MParameters}
    \param{part, partin}
    \eng{any lists denoting partitions}
    \param{n}
    \eng{any non negative integer}
  \end{MParameters}
  \begin{MOptions}
    \option{\weight=w}
    \eng{weight of listed partitions is \Mpar{w}}
    \option{\nb}
    \eng{only counts objects}
  \end{MOptions}


  \vspace*{1ex}
  \Mwarning{%
    Use the syntax \Mex{hold(identifier)}, instead of \Mex{identifier},
    if one of the identifiers above is already defined.
    }

  \begin{MIntro}
    \eng{The {\Mthis} function gives all partitions contained into the
      diagram of a given partition.  The list is ordered by increasing
      length.
 
      Called with a second argument \Mex{Partin}, the function returns
      the list of all partitions contained into the diagram of
      \Mex{part} and containing the diagram of \Mex{partin}.}
  \end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::PART::ListPartIn( [3,1] );
\end{Mexin}
\begin{Mexout}
          [[], [1], [2], [3], [1, 1], [2, 1], [3, 1]]
\end{Mexout}
\begin{Mexin}
muEC::PART::ListPartIn( [3,2,1], [2,1,1] );
\end{Mexin}
\begin{Mexout}
         [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 2, 1]]
\end{Mexout}
\begin{Mexin}
muEC::PART::ListPartIn( [4,3,2], weight=6 );
\end{Mexin}
\begin{Mexout}
       [[4, 2], [3, 3], [4, 1, 1], [3, 2, 1], [2, 2, 2]]
\end{Mexout}
\begin{Mexin}
muEC::PART::ListPartIn( [40,30,15,10,8,7,5,3,1], nb );
\end{Mexin}
\begin{Mexout}
                            9631414
\end{Mexout}
\end{MExample}

\MRelatedFunctions{ListPart,ListSkewDiag,TYP::IsPart}
\end{Mhelppage}
