% $Date: 2003/09/15 16:37:46 $ $Author: nthiery $ $Revision: 1.1.1.1 $

\begin{Mhelppage}{IsRegPart}%
  {V. Prosper}%
  \begin{MInfo}
    \eng{tests whether the argument is a \Mex{n}-regular partition}
  \end{MInfo}
  

\begin{MCalls}
\Mcall{n}
\Mcall{part}
\end{MCalls}

\begin{MParameters}
  \param{n}
  \eng{a positive integer}
  \param{expr}
  \eng{a partition}
\end{MParameters}

\begin{MIntro}
  \eng{
The {\Mthis} function tests whether \Mex{expr} is a \Mex{n}-regular partition,
that is a  partition such that it has no part repeated more than \Mex{n}-1
times, or equivalently, if the difference between any two consecutive parts of
the conjugate partition are strictly less than \Mex{n}.

}
\end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::PART::Part2Conjugate( [3, 3, 2, 2, 1, 1] );
\end{Mexin}
\begin{Mexout}
                           [6, 4, 2]
\end{Mexout}
\begin{Mexin}
muEC::TYP::IsRegPart( 2, [3, 3, 2, 2, 1, 1] );
\end{Mexin}
\begin{Mexout}
                             FALSE
\end{Mexout}
\begin{Mexin}
muEC::TYP::IsRegPart( 3, [3, 3, 2, 2, 1, 1] );
\end{Mexin}
\begin{Mexout}
                             TRUE
\end{Mexout}
\end{MExample}

\MRelatedFunctions{PART::Part2Conjugate,PART::ListPart,IsPart}
\end{Mhelppage}
