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

\begin{Mhelppage}{SkewPart2Mat}{V. Prosper}

  \begin{MInfo}
    \eng{a planar representation of a skew partition}
  \end{MInfo}

  \MDeclareOption{\alphabet}{alphabet}

  \begin{MCalls}
    \Mcall{skp\Mopt{,\alphabet=l}}
  \end{MCalls}

  \begin{MParameters}
    \param{skp}
    \eng{a skew part}
  \end{MParameters}
  \begin{MOptions}
    \option{alphabet=l}
    \eng{\Mpar{l} is a list  of 1 to 3 components,
      \Mmath{l[1]}{l_1} filling the skew diagram,
      \Mmath{l[2]}{l_2} the inner diagram and
      \Mmath{l[3]}{l_3} the outside}
  \end{MOptions}
  
  \begin{MIntro}
    \eng{The {\Mthis} function gives a planar representation of a skew
      partition in the Cartesian plane, i.e. the north-east quadrant.
      
      A skew partition is a list of two partitions \Mex{p1} and
      \Mex{p2} such that \Mex{p1} is greater than \Mex{p2} (with
      respect to inclusion of diagrams).  }
  \end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::PART::SkewPart2Mat( [[3,2],[2]] );
\end{Mexin}
\begin{Mexout}
                         +-         -+
                         |  1, 1, 0  |
                         |           |
                         |  0, 0, 1  |
                         +-         -+
\end{Mexout}
\begin{Mexin}
print(Unquoted, muEC::PART::SkewPart2Mat( [[3,2],[2]], alphabet=["#",".",""] )):
\end{Mexin}
\begin{Mexout}
                         +-         -+
                         |  #, #,    |
                         |           |
                         |  ., ., #  |
                         +-         -+
\end{Mexout}
\begin{Mexin}
map( muEC::PART::ListSkewDiag(3),muEC::PART::SkewPart2Mat )
\end{Mexin}
\begin{Mexout}
--                                            +-         -+
|               +-         -+  +-         -+  |  1, 0, 0  |
|  +-       -+  |  1, 0, 0  |  |  1, 1, 0  |  |           |
|  | 1, 1, 1 |, |           |, |           |, |  0, 1, 0  |,
|  +-       -+  |  0, 1, 1  |  |  0, 0, 1  |  |           |
|               +-         -+  +-         -+  |  0, 0, 1  |
--                                            +-         -+

                           +-      -+  +-      -+  +-   -+ --
   +-      -+  +-      -+  |  1, 0  |  |  1, 0  |  |  1  |  |
   |  1, 0  |  |  1, 1  |  |        |  |        |  |     |  |
   |        |, |        |, |  0, 1  |, |  1, 0  |, |  1  |  |
   |  1, 1  |  |  0, 1  |  |        |  |        |  |     |  |
   +-      -+  +-      -+  |  0, 1  |  |  0, 1  |  |  1  |  |
                           +-      -+  +-      -+  +-   -+ --
\end{Mexout}
\end{MExample}

\MRelatedFunctions{ListSkewDiag,Part2Mat,TYP::IsSkewDiag,TYP::IsSkewPart}
\end{Mhelppage}
