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%                                                                             %
% young.sty                                                                   %
%                                                                             %
% version 0.67                                                                %
%                                                                             %
% Copyright 2011 Kevin Purbhoo                                                %
% Licence: GNU general public licence version 2                               %
%                                                                             %
% This is an EXTENSIVELY modified version of                                  %
%     YOUNG.STY by J"org Knappen 7-feb-1992                                   %
%     Licence: GNU licence version 2                                          %
%     based on YOUNG.TEX                                                      %
%     macro to make Young tableaux                                            %
%     by:  Paul E. S. Wormer  <U644301@HNYKUN11>                              %
%                                                                             %
%                                                                             %
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%                                                                             %
%                                                                             %
%    This program is free software: you can redistribute it and/or modify     %
%    it under the terms of the GNU General Public License as published by     %
%    the Free Software Foundation, version 2.                                 %
%                                                                             %
%    This program is distributed in the hope that it will be useful,          %
%    but WITHOUT ANY WARRANTY; without even the implied warranty of           %
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the            %
%    GNU General Public License for more details.                             %
%                                                                             %
%    You should have received a copy of the GNU General Public License        %
%    along with this program.  If not, see <http://www.gnu.org/licenses/>.    %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Global color variables
%
\newcommand*{\yshadecolorbg}{}
\newcommand*{\yshadecolorfg}{}
\newcommand*{\YShadeColorBg}{}
\newcommand*{\YShadeColorFg}{}
\newcommand*{\YSHADECOLORFG}{}
\newcommand*{\YSHADECOLORBG}{}
\newcommand*{\yaltshadecolorbg}{}
\newcommand*{\yaltshadecolorfg}{}
\newcommand*{\YAltShadeColorBg}{}
\newcommand*{\YAltShadeColorFg}{}
\newcommand*{\YALTSHADECOLORFG}{}
\newcommand*{\YALTSHADECOLORBG}{}
%
% Commands to set colors
%
\newcommand*{\ysetshade}[2][]{%
  \def\yshadecolorfg{#1}%
  \def\yshadecolorbg{#2}%
}
\newcommand*{\YSetShade}[2][]{%
  \def\YShadeColorFg{#1}%
  \def\YShadeColorBg{#2}%
}
\newcommand*{\YSETSHADE}[2][]{%
  \def\YSHADECOLORFG{#1}%
  \def\YSHADECOLORBG{#2}%
}
\newcommand*{\ysetaltshade}[2][]{%
  \def\yaltshadecolorfg{#1}%
  \def\yaltshadecolorbg{#2}%
}
\newcommand*{\YSetAltShade}[2][]{%
  \def\YAltShadeColorFg{#1}%
  \def\YAltShadeColorBg{#2}%
}
\newcommand*{\YSETALTSHADE}[2][]{%
  \def\YALTSHADECOLORFG{#1}%
  \def\YALTSHADECOLORBG{#2}%
}
%
%  Default options for young environment
%
\newcommand*{\y@defaultcellsize}{2.8ex}
\newcommand*{\y@defaultposition}{b}
\newcommand*{\youngspecial}{,;=!?^_}
\newcommand*{\y@hwratio}{1:1}
\newcommand*{\y@everycell}{}
\newcommand*{\y@everyframe}{}
%
% Commands for setting them
%
\newcommand*{\ydefaultcellsize}[1]{\def\y@defaultcellsize{#1}}
\newcommand*{\ydefaultposition}[1]{\def\y@defaultposition{#1}}
\newcommand*{\yhwratio}[1]{\def\y@hwratio{#1}}
\newcommand*{\yeverycell}[1]{\def\y@everycell{#1}}
\newcommand*{\yeveryframe}[1]{\def\y@everyframe{#1}}
%
% public lengths
%
\newlength\ybaselineoffset     \setlength{\ybaselineoffset}{.75ex}
\newlength\yframethickness     \setlength{\yframethickness}{0.5pt}
\newlength\yautosizeminimum    \setlength{\yautosizeminimum}{2.8ex}
\newlength\ycellpadding        \setlength{\ycellpadding}{0.3ex} 
%
% A counter that get's incremented with every \begin{young}
%
\newcounter{youngcounter}
%
%  Commands to set formatting for cells drawn in the young environment
%
\newcommand\yframe{%  cell with a frame
   \gdef\y@draw@left{l}%
   \gdef\y@draw@right{r}%
   \gdef\y@default@draw@state{}%
   \gdef\y@use@default@draw{}%
}
\newcommand\ynoframe{%  cell with no frame
   \global\let\y@box@cmd\y@nofbox%
   \gdef\y@use@default@draw{}%
}
\newcommand\ynoright{%
   \gdef\y@draw@left{l}%
   \gdef\y@draw@right{}%
   \gdef\y@default@draw@state{[}%
   \gdef\y@use@default@draw{}%
}
\newcommand\ynoleft{%
   \gdef\y@draw@left{}%
   \gdef\y@draw@right{r}%
   \gdef\y@default@draw@state{]}%
   \gdef\y@use@default@draw{}%
}
\newcommand\ynoleftright{%
   \gdef\y@draw@left{}%
   \gdef\y@draw@right{}%
   \gdef\y@default@draw@state{=}%
   \gdef\y@use@default@draw{}%
}
\newcommand\ynotop[1][]{%
   \def\y@patch{#1}
   \ifx\y@patch\empty%
      \gdef\y@dont@draw@top{y}%
   \else
      \gdef\y@dont@draw@top{#1}%
   \fi%
}
\newcommand\ywithtop{%
   \gdef\y@dont@draw@top{}%
}
\newcommand\ynobottom[1][]{%
   \def\y@patch{#1}
   \ifx\y@patch\empty%
      \gdef\y@dont@draw@bottom{y}%
   \else
      \gdef\y@dont@draw@bottom{#1}%
   \fi%
}
\newcommand\ywithbottom{%
   \gdef\y@dont@draw@bottom{}%
}
\def\y@shadeopt[#1]{%
   \xdef\y@shade@color@fg{}%
   \xdef\y@shade@color@bg{#1}}%
\def\y@shadenoopt{%
   \xdef\y@shade@color@fg{\yshadecolorfg}%
   \xdef\y@shade@color@bg{\yshadecolorbg}%
}
\newcommand\yshade[1][@@@@]{%  Shade cell in color ##1 if specified
   \def\y@stringa{@@@@}%       or colors set by \ysetshade otherwise
   \def\y@stringb{#1}%
   \ifx\y@stringa\y@stringb%
       \y@shadenoopt%
   \else%
       \y@shadeopt[#1]%
   \fi%
}
\newcommand\YShade{%    Shaded cell in color set by \YSetShade
   \ifx\YShadeColorFg\empty%
      \xdef\y@shade@color@fg{\yshadecolorfg}%
   \else%
      \xdef\y@shade@color@fg{\YShadeColorFg}%
   \fi%
   \xdef\y@shade@color@bg{\YShadeColorBg}%
}
\newcommand\YSHADE{%    Shaded cell in color set by \YSETSHADE
   \ifx\YSHADECOLORFG\empty%
      \ifx\YShadeColorFg\empty%
         \xdef\y@shade@color@fg{\yshadecolorfg}%
      \else%
         \xdef\y@shade@color@fg{\YShadeColorFg}%
      \fi%
   \else%
      \xdef\y@shade@color@fg{\YSHADECOLORFG}%
   \fi%
   \xdef\y@shade@color@bg{\YSHADECOLORBG}%
}
\newcommand\yaltshade{%  Shaded cell in color set by \ysetaltshade
   \xdef\y@shade@color@fg{\yaltshadecolorfg}%
   \xdef\y@shade@color@bg{\yaltshadecolorbg}%
}
\newcommand\YAltShade{%   Shaded cell in color set by \YSetAltShade
   \ifx\YAltShadeColorFg\empty%
      \xdef\y@shade@color@fg{\yaltshadecolorfg}%
   \else%
      \xdef\y@shade@color@fg{\YAltShadeColorFg}%
   \fi%
   \xdef\y@shade@color@bg{\YAltShadeColorBg}%
}
\newcommand\YALTSHADE{%    Shaded cell in color set by \YSETSHADE
   \ifx\YALTSHADECOLORFG\empty%
      \ifx\YAltShadeColorFg\empty%
         \xdef\y@shade@color@fg{\yaltshadecolorfg}%
      \else%
         \xdef\y@shade@color@fg{\YAltShadeColorFg}%
      \fi%
   \else
      \xdef\y@shade@color@fg{\YALTSHADECOLORFG}%
   \fi%
   \xdef\y@shade@color@bg{\YALTSHADECOLORBG}%
}
\newcommand\ynoshade{%
   \xdef\y@shade@color@fg{}%
   \xdef\y@shade@color@bg{}%
}
\newcommand\yvalignincell[1]{%
   \xdef\y@valign@cell{#1}%
}
\newcommand\yrighttoleft{%
   \xdef\y@order@right@to@left{y}%
}
%
% Commands used for autosizing
%
\newcounter{young@auto}%  Keeps track of autosized tableaux
\newcounter{last@young@auto}%  Keeps track of how many there were last time
\newcommand*{\y@autosizedata}[4]{%  
  \global\@namedef{y@auto@#1}{#3}%
  \global\@namedef{y@autowarn@#2}{#4}%
  \global\@namedef{y@autoname@#2}{#1}%
  \stepcounter{last@young@auto}%
}%
    % This command is used by the .aux file.  
    % Three macros are declared.  The first allows us to lookup the cell size 
    % of a tableau by its label.  The second does lookup by counter.
    % The third allows us to lookup of label name using the counter.
    % Since more than one tableau may have the same label, the results
    % of the first two lookups may not always agree.  By-label lookup is used 
    % to set the cell size.  The other two are used to check if things have
    % changed since the last run.
\newif\if@y@autosize@warning%   Becomes true if we need to generate
\@y@autosize@warningfalse%      a warning at the end of document
\newif\if@y@use@autosize%       True if cell size is "auto" or "auto=<label>"
\AtEndDocument{%   Make a warning at the end of document, if necessary
      \def\@xgobble#1{{\setbox0\hbox{#1}}}%
      \@xgobble{%  Don't produce output, because i don't trust \ifnum
      % produce if there were a different number of autosizes than last time
      \ifnum\thelast@young@auto=\theyoung@auto\relax\else%
          \global\@y@autosize@warningtrue\fi%
      }%
      \if@y@autosize@warning%
        \PackageWarningNoLine{young.sty}% make the warning
        {Autosizing data have changed or are not available. %
        You may need to rerun LaTeX to get cell sizes right}%
      \fi%
}%
%
%
% private lengths
%
\newlength\y@cell@size        % (vertical) cell size excluding the frame
\newlength\y@withf@size       % cell size including the frame
\newlength\y@hcell@size       % horizontal cell size excluding the frame
\newlength\y@hwithf@size      % horizontal size including the frame
\newlength\y@below@amt        % amount below the baseline
\newlength\y@above@amt        % amount above the baseline
\newlength\y@abovewithf@amt   % amount below the baseline, including frame
\newlength\y@belowwithf@amt   % amount above the baseline, including frame
\newlength\y@templen          % a temporary length variable
\newlength\y@maxentry@size    % the size of the largest cell seen so far
\newlength\@y@maxentry@size 
\newlength\y@lastmaxentry@size % the size of the largest cell seen so far
\newlength\@y@lastmaxentry@size
%
% Some boxes that will be handy
%
\newsavebox\young@box%
\newsavebox\y@current@box%
\newsavebox\y@reverse@box%
\newsavebox\@y@reverse@box%
%
%  These commands are used as global variables by the environment
%
\newcommand{\y@box@cmd}{}%          what basic type (frame or no frame)?
\newcommand{\y@valign@cell}{}%      vertical alignment of entry in the cell
\newcommand{\y@shade@color@fg}{}%   foreground color
\newcommand{\y@shade@color@bg}{}%   background color
\newcommand{\y@draw@left}{}%          should we draw the left side?
\newcommand{\y@draw@right}{}%         should we draw the right side?
\newcommand{\y@dont@draw@top}{}%      should we draw the top?
\newcommand{\y@dont@draw@bottom}{}%   should we draw the bottom?
\newcommand{\y@default@draw@state}{}% the default if no options are given
\newcommand{\y@use@default@draw}{}%   should we use the default?
\newcommand{\y@at@eol}{}%             are we at the end of line?
%
%
%  THE MAIN ENVIRONMENT
%
\newenvironment{young}[1][\y@defaultcellsize]{%  This extra relaying
  \def\y@@optargI{#1}\begin{young@relay}%        circumvents a bug
}%                                               in which an error occurs
{\end{young@relay}}%                             when the first cell is
%                                                empty and the optional
\newenvironment{young@relay}[1][\y@defaultcellsize]{%  arguments aren't
   \begin{@young}[\y@@optargI][#1]%                    specified.  This
}%                                           is a hack, but I have no idea
{\end{@young}}%                              how to fix it properly.
%
\newenvironment{@young}[1][\y@defaultcellsize]{%
%  There are actually two optional arguments---the second argument is
%  provided by a relay mechanism
  \stepcounter{youngcounter}%              increment the counter
  \vrule height 0pt width 0pt depth 0pt%   switch tex into horizontal mode
  \begingroup%
  \def\y@optargI{#1}%
  \let\@y@box@cmd\y@box@cmd%                save "global variables"
  \let\@y@valign@cell\y@valign@cell%        just in case somebody wants
  \let\@y@shade@color@fg\y@shade@color@fg%  to nest the environment
  \let\@y@shade@color@bg\y@shade@color@bg%  nest this environment, i.e.
  \let\@y@draw@left\y@draw@left%            create a tableau whose
  \let\@y@draw@right\y@draw@right%          entries are young tableaux.
  \let\@y@default@draw@state\y@default@draw@state%  (this actually works!
  \let\@y@use@default@draw\y@use@default@draw%      you just need to 
  \let\@y@dont@draw@top\y@dont@draw@top%            enclose the inside
  \let\@y@dont@draw@bottom\y@dont@draw@bottom%      environment in braces.)
  \let\@y@at@eol\y@at@eol%                     saving is local so that it
  \let\@y@order@right@to@left\y@order@right@to@left%   doesn't clobber
  \setlength\@y@maxentry@size\y@maxentry@size%         anything
  \setlength\@y@lastmaxentry@size\y@lastmaxentry@size%  
  \setbox\@y@reverse@box\box\y@reverse@box%
  \begin{@young@relay}% 
}% 
  {\end{@young@relay}%
  \global\let\y@box@cmd\@y@box@cmd%           restore global variables
  \global\let\y@valign@cell\@y@valign@cell%   
  \global\let\y@shade@color@fg\@y@shade@color@fg%
  \global\let\y@shade@color@bg\@y@shade@color@bg%
  \global\let\y@draw@left\@y@draw@left%
  \global\let\y@draw@right\@y@draw@right%
  \global\let\y@default@draw@state\@y@default@draw@state%
  \global\let\y@use@default@draw\@y@use@default@draw%
  \global\let\y@dont@draw@top\@y@dont@draw@top%
  \global\let\y@dont@draw@bottom\@y@dont@draw@bottom%
  \global\let\y@at@eol\@y@at@eol%
  \global\let\y@order@right@to@left\@y@order@right@to@left% 
  \global\setlength\y@maxentry@size\@y@maxentry@size%
  \global\setlength\y@lastmaxentry@size\@y@lastmaxentry@size%
  \global\setbox\y@reverse@box\box\@y@reverse@box%
  \endgroup}
%
\newenvironment{@young@relay}[1][\y@defaultcellsize]{%
  %
  % parse arguments: one arg is position, other is cell size
  % they can come in either order
  % first figure out what position is suppposed to be
  %
  \def\y@optargII{#1}%
  \def\y@begin@vert@align{}%
  \def\y@setvalignment##1{%
    \edef\y@optstring{##1}%
    \def\y@optionc{c}%
    \def\y@optiont{t}%
    \def\y@optionb{b}%
    \def\y@optionbb{bb}%
    \def\y@optiontt{tt}%
    \ifx\y@optstring\y@optionc%
      \ifmmode%
         \def\y@begin@vert@align{\vcenter\bgroup}%
         \def\y@end@vert@align{\egroup}%
      \else%
         \def\y@begin@vert@align{\begin{math}\vcenter\bgroup}%
         \def\y@end@vert@align{\egroup\end{math}}%
      \fi%
    \else\ifx\y@optstring\y@optiontt%
      \def\y@begin@vert@align{\lower\y@withf@size\hbox\bgroup\vtop\bgroup}%
      \def\y@end@vert@align{\egroup\egroup}%
    \else\ifx\y@optstring\y@optiont%
      \def\y@begin@vert@align{\lower\y@belowwithf@amt\hbox\bgroup\vtop\bgroup}%
      \def\y@end@vert@align{\egroup\egroup}%
    \else\ifx\y@optstring\y@optionbb%
      \def\y@begin@vert@align{\vbox\bgroup}%
      \def\y@end@vert@align{\egroup}%
    \else\ifx\y@optstring\y@optionb%
      \def\y@begin@vert@align{\lower\y@belowwithf@amt\hbox\bgroup\vbox\bgroup}%
      \def\y@end@vert@align{\egroup\egroup}%
    \fi\fi\fi\fi\fi%
  }%
  \y@setvalignment\y@optargI%         try using arg 1 as position
  \ifx\y@begin@vert@align\empty%  if that didn't work
     \y@setvalignment\y@optargII%     try using arg 2
     \ifx\y@begin@vert@align\empty%      if that didn't work
       \y@setvalignment\y@defaultposition%  try using \y@defaultposition
       \ifx\y@begin@vert@align\empty%     if that didn't work
         \y@setvalignment{b}%               fall back to position = b
       \fi%
     \fi%
     \edef\y@optargII{\y@optargI}% arg 1 wasn't position, assume it's size
  \fi%
  %
  % Set the cell size, which is now in \y@optargII.  If auto is given 
  % as size, check to see if a label is specified.  If so, use this 
  % label to look it up based on data from the .aux file.  Otherwise, 
  % use \theyoung@auto counter as the label.
  %
  \def\y@checkifauto##1{\expandafter\y@@checkifauto##1@@@@@@]}%
       % pad the label name with six @-signs to make sure we pass at least
       % six characters to \y@@checkifauto
  \def\y@@checkifauto##1##2##3##4##5##6]{%
    \def\y@autostring{auto}%
    \def\y@initstring{##1##2##3##4}%
    \ifx\y@initstring\y@autostring%  if "auto" given as size
      \stepcounter{young@auto}%
      \edef\y@autowarn@label{\theyoung@auto}%
      \@y@use@autosizetrue%
       \if##5=% if a label was specified
          \def\y@autosize@label{##6}%
          \@ifundefined{y@@auto@##6}{%  if we haven't seen this label yet
             \expandafter\def\csname y@@auto@##6\endcsname{0pt}% remember it
          }{%  if we have seen this same label before
            %  look up the largest entry produced under this label
             \edef\y@last@maxsize{\csname y@@auto@##6\endcsname}%
             \global\setlength{\y@lastmaxentry@size}{\y@last@maxsize}%
          }%
       \else%  otherwise just use the counter as the label
          \edef\y@autosize@label{\theyoung@auto}%
       \fi%
    \else% otherwise, we're not autosizing
       \@y@use@autosizefalse
    \fi%
  }%
  \def\y@setcellsize##1{%  set the cell size by looking up macro ##1
    \ifx##1\relax%
      \setlength{\y@cell@size}{0pt}%
    \else%
      \setlength{\y@cell@size}{##1}%
    \fi%
  }%
  \global\setlength{\y@maxentry@size}{0pt}%
  \global\setlength{\y@lastmaxentry@size}{0pt}%
  \y@checkifauto\y@optargII%
  \if@y@use@autosize%
    \expandafter\y@setcellsize\csname y@auto@\y@autosize@label\endcsname%
    % set the cell size by looking it up.
    \addtolength{\y@cell@size}{2\ycellpadding}% add padding
    \ifdim\y@cell@size<\yautosizeminimum%  if it's still not big enough
       \setlength{\y@cell@size}{\yautosizeminimum}% make it the min size
    \fi%
  \else%  autosize not used, set cell size from arguments
    \setlength{\y@cell@size}{\y@optargII}%
  \fi%
  %
  % set all other relevant lengths
  %
  \def\y@@hwratio##1:##2]{\def\y@hratio{##1}\def\y@wratio{##2}}%
  \expandafter\y@@hwratio\y@hwratio]%
  \setlength{\y@withf@size}{\y@cell@size}%
    \addtolength{\y@withf@size}{2\yframethickness}%
  \setlength{\y@hcell@size}{\y@cell@size}%
    \multiply\y@hcell@size by \y@wratio%
    \divide\y@hcell@size by \y@hratio%
  \setlength{\y@hwithf@size}{\y@hcell@size}%
    \addtolength{\y@hwithf@size}{2\yframethickness}%
  \setlength{\y@below@amt}{0.5\y@cell@size}% 
    \addtolength{\y@below@amt}{-\ybaselineoffset}% 
    \ifdim\y@below@amt<0pt\setlength{\y@below@amt}{0pt}\fi%
  \setlength{\y@belowwithf@amt}{\y@below@amt}%  
    \addtolength{\y@belowwithf@amt}{\yframethickness}%  
  \setlength{\y@above@amt}{\y@cell@size}%
    \addtolength{\y@above@amt}{-\y@below@amt}% 
  \setlength{\y@abovewithf@amt}{\y@above@amt}%
    \addtolength{\y@abovewithf@amt}{\yframethickness}%
  %
  % Macros involved in drawing cells.
  %
  \def\y@drawentry{%  positions the entry within the cell and draw it
     \edef\y@cellpaddingskip{\the\ycellpadding}% because \hskip is picky
     \setbox\young@box\hbox to \y@hcell@size{% add fils and skips on both sides
        \hskip\y@cellpaddingskip plus 1fil minus\y@cellpaddingskip%
        \unhbox\young@box%
        \hskip\y@cellpaddingskip plus 1fil minus\y@cellpaddingskip%
     }%
     \addtolength{\y@above@amt}{-\ht\young@box}%  compute space above 
     \addtolength{\y@below@amt}{-\dp\young@box}%  and below the box
     \setlength{\y@templen}{\y@above@amt}%
     \addtolength{\y@templen}{\y@below@amt}%
     \ifdim\y@templen<2\ycellpadding%  if it's too big
         \def\y@valign@cell{c}%        just center it
     \else\ifdim\y@above@amt<\ycellpadding%  if it goes too high
         \def\y@valign@cell@{t}%       align top with top
     \else\ifdim\y@below@amt<\ycellpadding%  if it goes to low
         \def\y@valign@cell@{b}%       align bottom with bottom
     \fi\fi\fi%
     \if\y@valign@cell c%
         \setlength{\y@templen}{\y@above@amt}%
         \addtolength{\y@templen}{-\y@below@amt}%
         \raise0.5\y@templen\box\young@box%
     \else\if\y@valign@cell t%
         \addtolength{\y@above@amt}{-\ycellpadding}%
         \raise\y@above@amt\box\young@box%
     \else\if\y@valign@cell b%
         \addtolength{\y@below@amt}{-\ycellpadding}%
         \lower\y@below@amt\box\young@box%
     \else%
         \box\young@box%
     \fi\fi\fi%
  }%
  \def\y@nofbox{%   Cell with no frame
     \vbox{\offinterlineskip%
     \hbox to \y@hwithf@size{%
     \vrule height\y@abovewithf@amt%
            width 0pt%
            depth\y@belowwithf@amt% 
     \kern\yframethickness%
     \y@drawentry%
     \kern\yframethickness}%
     \hrule height 0pt}%
  }%
  \def\y@patchcorners##1{% 
     \edef\y@patcharg{##1}%
     % look for "l" in the argument
     \expandafter\in@\expandafter l\expandafter{\y@patcharg}\ifin@%
     % if found, patch the left corner if found
        \hbox{%
        \begin{picture}(0,0)(0,0)%
        \put(0,0){\vrule height 0pt%
                          width \yframethickness%
                          depth \yframethickness}%
        \end{picture}%
        }%
     \fi
     % look for "r" in the argument
     \expandafter\in@\expandafter r\expandafter{\y@patcharg}\ifin@%
     % if found, patch the right corner if found
        \hbox{%
        \begin{picture}(0,0)(0,0)%
        \put(0,0){\kern\yframethickness\kern\y@hcell@size%
                  \vrule height 0pt%
                          width \yframethickness%
                          depth \yframethickness}%
        \end{picture}%
        }%
     \fi
  }%
  \def\y@switchleftandright{%
     \if\y@draw@left l\ifx\y@draw@right\empty%
         \def\y@draw@left{}\def\y@draw@right{r}%
     \fi\else\ifx\y@draw@left\empty\if\y@draw@right r%
         \def\y@draw@left{l}\def\y@draw@right{}%
     \fi\fi\fi%
     \if\y@dont@draw@top l%
         \def\y@dont@draw@top{r}%
     \else\if\y@dont@draw@top r%
         \def\y@dont@draw@top{l}%
     \fi\fi%
     \if\y@dont@draw@bottom l%
         \def\y@dont@draw@bottom{r}%
     \else\if\y@dont@draw@bottom r%
         \def\y@dont@draw@bottom{l}%
     \fi\fi%
  }%
  \def\y@fbox{%  Cell with a frame
     \if\y@order@right@to@left y%
        \y@switchleftandright%
     \fi%
     \ifx\y@shade@color@bg\empty\else%
        \begin{picture}(0,0)(0,0)%  do the shading.  picture is an easy
        \put(0,0){{\color{\y@shade@color@bg}%        way to draw something
        \kern0.5\yframethickness%                    bigger than the box
        \addtolength{\y@withf@size}{-0.5\yframethickness}%  it naturally
        \addtolength{\y@hcell@size}{\yframethickness}%      fits in.
        \vrule height\y@withf@size%
               width\y@hcell@size%
               depth -0.5\yframethickness}}%
        \end{picture}%
     \fi%
     \vbox{\offinterlineskip%  
     \ifx\y@dont@draw@top\empty%
         \hrule height\yframethickness%  draw the top line
     \else%   otherwise patch corners...
         \y@patchcorners{\y@dont@draw@top\y@draw@left\y@draw@right}% 
         \kern\yframethickness% ...but don't draw the line
     \fi%
     \hbox to \y@hwithf@size{%
     \ifx\y@draw@left\empty%
         \vrule height\y@above@amt% create the space
                width 0pt%          but don't draw anything
                depth\y@below@amt%
         \kern\yframethickness%   
     \else%
         \vrule height\y@above@amt%   draw the left side
                width\yframethickness%
                depth\y@below@amt%
     \fi%
     \begingroup%
     \ifx\y@shade@color@fg\empty\else%
       \color{\y@shade@color@fg}%  set foreground color
     \fi% 
     \y@drawentry%  draw entry
     \endgroup%
     \ifx\y@draw@right\empty%
         \vrule height\y@above@amt%
                width 0pt%
                depth\y@below@amt%
         \kern\yframethickness%
     \else%
         \vrule height\y@above@amt%
                width\yframethickness%
                depth\y@below@amt%
     \fi%
     }% end the hbox
     \ifx\y@dont@draw@bottom\empty%
         \hrule height\yframethickness%  draw the bottom line
     \else%
         \y@patchcorners{\y@dont@draw@bottom\y@draw@left\y@draw@right}% 
         \kern\yframethickness%  patch corners but don't draw the line
     \fi%
     }% end the vbox
  }%
  %
  % The macros below read the cell entry, and decide what kind of
  % cell to draw.
  %
  \def\y@defaultdraw{%  picks what to draw if user hasn't specified anything.
                     %  depends on the current "state" and whether we're
                     %  at the end of line.  In theory, this algorithm
                     %  should default to the thing you want (at least
                     %  most of the time!).
     \if\y@default@draw@state[%
         \ifx\y@at@eol\empty%  
            \ynoleftright%                  draw =
            \gdef\y@default@draw@state{[}%  state [ -> [ if not end of line
         \else%        draw ]
            \ynoleft%  state [ -> ] if at end of line
         \fi%
     \else\if\y@default@draw@state]% 
         \ifx\y@at@eol\empty%   draw [
            \ynoright%          state ] -> [ if not at end of line
         \else%
            \yframe%                        draw {}
            \gdef\y@default@draw@state{]}%  state ] -> ] if at end of line
         \fi%
     \else\if\y@default@draw@state=%   draw =
         \ynoleftright%                state = -> =
     \else%                            draw {}
         \yframe%                      state {} -> {}
     \fi\fi\fi%
  }%
  \def\y@ifnextspecial##1##2##3{% matches the next character if it's special
      \def\y@argthen{##2}% otherwise \@gobble gobbles up the \else or \fi!
      \def\y@argelse{##3}%
      \@ifnextcharnoigsp##1{%
          \expandafter\in@\expandafter##1\expandafter{\youngspecial}%
          \ifin@\expandafter\y@argthen%
          \else\expandafter\y@argelse\fi}{##3}% 
  }%
  \def\y@initcell{% set defaults
      \gdef\y@at@eol{}%
      \gdef\y@use@default@draw{y}%
      \global\let\y@box@cmd\y@fbox%
      \gdef\y@shade@color@fg{}%
      \gdef\y@shade@color@bg{}%
      \gdef\y@order@right@to@left{}%
      \ywithtop\ywithbottom%
      \yvalignincell{}%
  }%
  \def\y@readentry{%  check for alignment characters
      %  check for <frame> characters
     \y@ifnextspecial,{\ynoframe\expandafter\y@@readentry\@gobble}{%  else
     \@ifnextcharnoigsp]{\expandafter\y@maybeleft\@gobble}{%  else
     \y@ifnextspecial={\expandafter\y@mayberight\@gobble}{%  else
     \y@ifnextspecial;{\yframe\expandafter\y@@readentry\@gobble}{%  else
     \y@@readentry}}}}%
  }%
  \def\y@@readentry{%  check for shading characters
     \y@ifnextspecial!{\expandafter\y@shbox\@gobble}{%  else
     \y@ifnextspecial?{\expandafter\y@shboxalt\@gobble}{%  else
     \y@@@readentry}}%
  }%
  \def\y@@@readentry{%  check for alignment characters
      \y@ifnextspecial_{\expandafter\y@vadown\@gobble}{%  else
      \y@ifnextspecial^{\expandafter\y@vaup\@gobble}{%  else
      \ignorespaces}}%
  }%
  % the rest of these macros continue parsing the formatting string
  \def\y@maybeleft{%
     \y@ifnextspecial={\expandafter\y@@maybeleft\@gobble}{% else
     ]}% put the ] back
  }%
  \def\y@@maybeleft{%
     \@ifnextcharnoigsp]{\yframe\expandafter\y@@readentry\@gobble}{% else
     \ynoright\y@@readentry}% put the ] back
  }%
  \def\y@mayberight{%
     \@ifnextcharnoigsp]{\ynoleft\expandafter\y@@readentry\@gobble}{% else
     \@ifnextcharnoigsp={\ynoleftright\expandafter\y@@readentry\@gobble}{% else
     =}}% put the = back
  }%
  \def\y@shbox{%   
     \def\yshadeand@@@read[####1]{\y@shadeopt[####1]\y@@@readentry}%
     \@ifnextcharnoigsp!{\expandafter\y@@shbox\@gobble}{%  else
     \@ifnextcharnoigsp[{\expandafter\yshadeand@@@read}{%  else
     \y@shadenoopt\y@@@readentry}}%
  }%
  \def\y@@shbox{%   
     \@ifnextcharnoigsp!{\YSHADE\expandafter\y@@@readentry\@gobble}{%  else
     \YShade\y@@@readentry}%
  }%
  \def\y@shboxalt{%
     \@ifnextcharnoigsp?{\expandafter\y@@shboxalt\@gobble}{% else
      \yaltshade\y@@@readentry}%
  }%
  \def\y@@shboxalt{%
     \@ifnextcharnoigsp?{\YALTSHADE\expandafter\y@@@readentry\@gobble}{% else
      \YAltShade\y@@@readentry}%
  }%
  \def\y@vadown{%
     \y@ifnextspecial^{\yvalignincell{c}%
                       \expandafter\ignorespaces\@gobble}{% else
     \yvalignincell{b}\ignorespaces}%
  }%
  \def\y@vaup{%
     \y@ifnextspecial_{\yvalignincell{c}%
                       \expandafter\ignorespaces\@gobble}{% else
     \yvalignincell{t}\ignorespaces}%
  }%
  %
  % main routine
  %
  \ifmmode%         figure out if we started in math mode or not
     \def\y@beginmathortext{$}%  if so, use math mode for entries
     \def\y@endmathortext{$}%
  \else%
     \def\y@beginmathortext{}%   otherwise don't
     \def\y@endmathortext{}%
  \fi%
  \hskip\yframethickness%
  \y@begin@vert@align%              begin vertically aligned box
  \offinterlineskip%
  \tabskip=-\yframethickness%   draw adjacent cell frames over top...
  \lineskip=-\yframethickness%  of one another to avoid double-thick lines
  \yframe%      make box with a frame the default
  \setbox\y@reverse@box\hbox{}%
  %
  %  mess with the definitions of \cr and \\ so we can recognize
  %  end of lines
  %
  \@ifundefined{y@@cr}{%  only do this once!
    \let\y@@cr\cr%  save \cr
    \def\cr{\gdef\y@at@eol{y}\y@@cr}% mark end of lines
  }{}%
  \let\y@@ss\\%     save \\
  \let\\\cr%        allow \\ to end lines, instead of \cr
  \everyvbox{\ifx\cr\\\let\\\y@@ss\fi\let\cr\y@@cr}% 
       % in theory, this should correctly restore \\ and \cr inside 
       % environments that might use them.  We only restore \\ if the
       % other environment hasn't already redefined it.
       % I haven't tested this exhaustively, but it seems to work
       % for tabular, parbox, matrix
  %
  \halign\bgroup%                      start halign environment
  %
  % preamble to halign
  % First read the next entry and put it in a box.
  % Use math mode if appropriate.
  %
  &\setbox\young@box\hbox{\y@beginmathortext%
      \begingroup\y@initcell\y@everycell\y@readentry##%
       \ifdim\lastskip>0pt\unskip\fi% unskip whitespace, not stretches
       \ifx\y@box@cmd\y@fbox\y@everyframe\fi%
      \endgroup%
     \y@endmathortext}%
  %
  \if\y@use@default@draw y%
      \y@defaultdraw%
      \gdef\y@use@default@draw{y}%
  \fi%
  %
  %  measure the size of the box
  %
  \setlength{\y@templen}{\wd\young@box}%   measure the width of the box
  \addtolength{\y@templen}{2\ycellpadding}%
  \multiply\y@templen by \y@hratio%
  \divide\y@templen by \y@wratio%
  \addtolength{\y@templen}{-2\ycellpadding}%
  \ifdim\y@templen>\y@maxentry@size%
     \global\setlength{\y@maxentry@size}{\y@templen}%
  \fi%
  %  The way we calculate vertical size depends on how the entry is aligned
  %  within the cell.  If it's the default, we measure both the height above
  %  the centerline, and the depth below the centerline, and use twice
  %  the larger as the vertical size.  Otherwise, we use the total of 
  %  height and depth.
  \ifx\y@valign@cell\empty%
    \setlength{\y@templen}{2\ht\young@box}%  measure the height
    \addtolength{\y@templen}{-2\ybaselineoffset}%
    \ifdim\y@templen>\y@maxentry@size%
       \global\setlength{\y@maxentry@size}{\y@templen}%
    \fi%
    \setlength{\y@templen}{2\dp\young@box}%  measure the depth
    \addtolength{\y@templen}{2\ybaselineoffset}%
    \ifdim\y@templen>\y@maxentry@size%
      \global\setlength{\y@maxentry@size}{\y@templen}%
    \fi%
  \else%
    \setlength{\y@templen}{\ht\young@box}%  measure the height
    \addtolength{\y@templen}{\dp\young@box}%  add the depth
    \ifdim\y@templen>\y@maxentry@size%
      \global\setlength{\y@maxentry@size}{\y@templen}%
    \fi%
  \fi%
  \ifdim\y@maxentry@size>\y@lastmaxentry@size%
     \global\setlength{\y@lastmaxentry@size}{\y@maxentry@size}%
  \fi%
  %
  %  Finally draw the box.
  %
  \setbox\y@current@box\hbox{\y@box@cmd}%  put the whole cell in a box
  \if\y@order@right@to@left y%             if we need to reverse boxes
	\ifx\y@at@eol\empty%                   if not at the end of line
      \global\setbox\y@reverse@box\hbox{%  prepend the box to beginning of the
         \box\y@current@box\hskip -\yframethickness\box\y@reverse@box}% sequence
      \kern\y@hwithf@size%                 make some space to put it in later
    \else%                                 if we are at the end of line
      \kern -\wd\y@reverse@box%            remove the empty space and put the
      \box\y@current@box\hskip -\yframethickness\box\y@reverse@box% sequence in
    \fi%
  \else%                               otherwise we're not reversing this box
    \kern -\wd\y@reverse@box%          draw any reversed boxes in the sequence
    \box\y@reverse@box\box\y@current@box%  followed by the current box
  \fi%
  %
  \unskip\crcr%     recognize end of line.
  %
  % This is the end of the preamble to halign.  Next come the
  % actual contents, supplied by the user.
}
{% close @young@relay environment
   \crcr% if the last line does not have a \\ or \cr, put one in
        % unfortunately it won't get noticed by the formatting processor
        % so we may need to make a correction after the fact
   %
   \egroup%       end halign environment
   %
   \ifx\y@at@eol\empty% if last \\ or \cr character was omitted
                      % we need to draw any boxes that were reversed
                      % and possibly patch up the last box drawn
                      % if default draw state ended in state [
     \if\y@order@right@to@left y%
          \setbox\young@box\lastbox%   remove the last box that TeX made
          \vskip \yframethickness%  undo the extra baseline skip that happens
          \hbox{\unhbox\young@box%   put in the reversed boxes.
          \kern -\wd\y@reverse@box%
          \if\y@use@default@draw y\if\y@default@draw@state[% patch the box first
             \vrule height \y@withf@size width \yframethickness depth 0pt%
          \else%
             \kern\yframethickness% 
          \fi\fi%
          \box\y@current@box\hskip -\yframethickness\box\y@reverse@box}%
     \else%
     \if\y@use@default@draw y\if\y@default@draw@state[% 
          \setbox\young@box\lastbox%   remove the last box that TeX made
          \vskip \yframethickness%  undo the extra baseline skip that happens
          \hbox{\unhbox\young@box%   patch up the box and put it back
          \vrule height \y@withf@size width \yframethickness depth 0pt}%
     \fi\fi\fi%
   \fi%
   \y@end@vert@align%       end the vbox
   \hskip\yframethickness%   undo the last tabskip
   %
   % If using autosizing, write autosize data to aux file.
   % Give a warning if the data have changed from last run.
   %
   \def\y@warnifwrong{%  
     \if@y@autosize@warning\else%  if we haven't made this warning already
       \expandafter\y@setcellsize%...
       \csname y@autowarn@\y@autowarn@label\endcsname% use counter to lookup
                                               % cell size from last time
       \ifdim\y@cell@size=\y@maxentry@size%
          \edef\y@oldlabel{\csname y@autoname@\y@autowarn@label\endcsname}%
          \ifx\y@oldlabel\y@autosize@label\else% if labels have changed 
             \global\@y@autosize@warningtrue%  need to make a warning
          \fi%
       \else% if cell size has changed
             \global\@y@autosize@warningtrue%  need to make a warning
        \fi%
     \fi
   }%
   \if@y@use@autosize%  if autosizing is enabled
     \expandafter\xdef\csname y@@auto@\y@autosize@label\endcsname{%
     \the\y@maxentry@size}%
     \protected@write\@auxout{}%  write relevant data to the .aux file
       {\string\y@autosizedata%   the string "\y@autosizedata"
        {\y@autosize@label}%      the label
        {\y@autowarn@label}%      the counter value
        {\the\y@lastmaxentry@size}%  the overall max entry size
        {\the\y@maxentry@size}}%  the max entry of this tableau
     \y@warnifwrong%  produce a warning if size has changed from last run
   \fi%
}
%
% provide "Young" as an alternate for "young"
%
\newenvironment{Young}[1][\y@defaultcellsize]{\begin{young}[#1]}{\end{young}}
%
%  Also recreate the \yng command from the youngtab package
%
\newcounter{y@rowsizecounter}
\newcommand\y@@@@@makerow{\ynoframe&}%  called if \y@makerow has blank argument
\newcommand\y@@@@makerow{&\y@@@makerow}% these two macros call each
\newcommand\y@@@makerow{%                other recursively to make the row
    \addtocounter{y@rowsizecounter}{-1}%
    \ifnum\they@rowsizecounter>0\relax%
        \expandafter\y@@@@makerow%  \expandafter in these macros ensures 
    \fi%                           \fi and \else are seen before the &
}
\newcommand\y@@makerow{% make a row length \they@rowsizecounter plus \cr
    \ifnum\they@rowsizecounter=0\relax%
       	\ynoframe% create a cell without frame, pretending to be an empty row
                 % really what I want is an \omit here, but TeX won't
                 % recognize it because by this point it's already read 
                 % some \edef and decide not to \omit.  I think one could 
                 % fix this by reading ahead an extra cell, and deciding 
                 % whether or not to put in the \omit before placing the 
                 % & ... but that just seems like waaaayyy to much work!
    \else%
        \expandafter\y@@@makerow%
	\fi\cr%    
}
\newcommand\y@makerow[1]{%  makes a row of (#1) cells
    \edef\y@therow{\expandafter\@firstofone#1\relax}% this ignores spaces...
	\edef\y@relaxed{\relax}%                          ... believe it or not
	\ifx\y@therow\y@relaxed%           if the entry is blank
        \expandafter\y@@@@@makerow%       make an cell without frame
	\else%
        \setcounter{y@rowsizecounter}{#1}% make a row of the 
		\expandafter\y@@makerow%           correct length
    \fi%
}
\def\y@@@@ng#1){\y@makerow{#1}\end{@young}\endgroup}
\def\y@@@ng#1,#2){\y@makerow{#1}\y@@ng(#2)}
\def\y@@ng(#1){%
   \edef\y@partition{#1}%
   \expandafter\in@\expandafter,\expandafter{\y@partition}%
   \ifin@%
       \expandafter\y@@@ng#1)% more than one row left
   \else%
       \expandafter\y@@@@ng#1)% just one row left
   \fi%
}
\newcommand{\y@ng}[1][\y@defaultcellsize]{%
\begin{@young}[\y@@optargI][#1]\y@@ng}%
\newcommand{\yng}[1][\y@defaultcellsize]{\begingroup%
   \def\y@@optargI{#1}%
   \y@ng%
}
%
%  This code is cut-and-pasted from the LaTeX kernel, with some minor
%  changes. This is just a modification of \@ifnextchar that doesn't 
%  gobble up spaces.  Because of this, use of reserved names should be 
%  quite safe here.
%
\def\@ifnextcharnoigsp#1#2#3{%
  \let\reserved@d=#1%
  \def\reserved@a{#2}%
  \def\reserved@b{#3}%
  \futurelet\@let@token\@ifnchnoigsp}%
\def\@ifnchnoigsp{%
    \ifx\@let@token\reserved@d%
      \let\reserved@c\reserved@a%
    \else%
      \let\reserved@c\reserved@b%
    \fi%
  \reserved@c}
%
%
\endinput
%

--------------------------------------------------------------------
Documentation:


                       *****************

If you're looking at this for the first time, you probably want to
go straight to the "Example", which is at the end.

                       *****************

In the recent past, I have found myself needing to create skew tableaux, 
with various colors and shaded boxes to distinguish different types 
of entries.  The creation of such diagrams in LaTeX has been a tedious 
process, as neither of the packages in the standard distribution of LaTeX
will do this.  The main purpose of writing this package was to provide 
a mechanism for doing this very easily.

The "young" package, has a nice tabular-like interface but no bells 
and whistles.  The syntax allows you to put just about any LaTeX code 
into any cell (but since the cell size is fixed, it's hard to take
full advantage of this).  The "youngtab" package is more comprehensive 
in its capabilities, but the contents of a cell must be represented 
by a single token, which can be frustrating if you find yourself needing 
to make a new command for every cell.

This package is intended to be an extension of (and in the parlance of 
the LaTeX Project Public Licence a "direct replacement for") the original 
"young" package, which has comparable functionality to the "youngtab" 
package.  I have tried to set things up so that any backwards 
compatibility issues should be rare, and easily resolved if they do arise.

--------------------------------------------------------------------
Enivironments:

\begin{young}[<position>][<cell size>]
<entry> & <entry> & ... \\
<entry> & <entry> & ... \\
...
 \end{young}

Creates a Young tableau.

<cell size> specifies the size of the cell.  This can be a length,
or {auto} or {auto=<label>}, which invokes the autosizing mechanism 
(see "Autosizing" below).  The command \ydefaultcellsize sets the
default value.  If the height to width ratio given set by \yhwratio 
is not 1:1, <cell size> means the height of the cell, and the 
width is determined by the ratio.

<position> specifies which part of the tableau should be aligned with
the rest of the line.  Valid options are:
   b   : bottom--align baseline with cell entries of bottom row
   c   : center
   t   : top--align baseline with cell entries of top row
   bb  : very bottom--align baseline with bottom of tableau
   tt  : very bottom--align baseline with top of tableau 
The command \ydefaultposition sets the default.

Optional arguments may be specified in either order, and either may
omitted.  


The entries are of the form:

    <entry> = <formatting><cell contents>

The formatting string is of the form:
 
    <formatting> = <frame><shading><alignment> 

Any or all of these may be omitted, but they must specified in the 
order above.  Spaces are (deliberately) not allowed.

<frame> may be one of:
,        : create a cell with no frame (cannot be shaded)
; or ]=] : create a cell with a frame
==       : cell with frame missing left and right sides 
]=       : cell with frame missing right side
=]       : cell with frame missing left side

These behave identically to the commands \ynoframe, \yframe, 
\ynoleftright, \ynoright and \ynoleft respectively.

If none is specified and no framing command is given anywhere in the 
<cell contents>, the default behaves according to the finite
state machine rules below.

    first frame      ->  frame ]=], state ]=]
       state ]=]     ->  frame ]=], state ]=]
       state ==      ->  frame ==, state ==
       state ]=      ->  frame ==, state ]=     (not at end of line)
       state ]=,EOL  ->  frame =], state =]     (at end of line)
       state =]      ->  frame ]=, state ]=     (not at end of line)
       state =],EOL  ->  frame ]=], state =]    (at end of line)
`
Explicitly specifying the frame type also puts the state machine into 
the specifed state for the next frame.  These rules make it quite easy
to draw objects like tabloids.  (See "Example", below.)


For cells with a frame or partial frame, <shading> may be one of:
!       : create a shaded cell with colors specified by \ysetshade
!!      : create a shaded cell with colors specified by \YSetShade
!!!     : create a shaded cell with colors specified by \YSETSHADE
?       : create a shaded cell with colors specified by \ysetaltshade
??      : create a shaded cell with colors specified by \YSetAltShade
???     : create a shaded cell with colors specified by \YSETALTSHADE
![<bg>] : create a shaded cell with background color <bg>

These behave identically to \yshade, \YShade, \YSHADE, \yaltshade,
\YAltShade, \YALTSHADE and \yshade[<bg>] respectively.

If none is specifed, or the relevant colors have not been set, the 
cell is drawn unshaded.  A cell without a frame can't be shaded, 
and <shading> will be ignored.  (The effect of a shaded cell with no frame 
can nevertheless be achieved using == (or \ynoleftright) with \ynotop 
and \ynobottom---it takes more work because it may also be necessary 
to patch corners.  See "Commands".)


<alignment> may be one of:
_        : place the entry at the bottom of the cell
^        : place the entry at the top of the cell
_^ or ^_ : vertically center the contents in the cell

These behave identically to \yvalignincell{b}, \yvalignincell{t}, 
\yvalignincell{c} respectively.

If none is specified, the default is to try to write the contents 
on the baseline of the cell, whose position is \ybaselineoffset below the 
center of the cell.  Normally, this should produce reasonably 
well-centered entries with a consistent baseline, which most of the
time is preferable over exact vertical centering.  However, if 
your entries involve vastly different font sizes, you may want to 
override this.  Other considerations, such as avoiding overfull
boxes, override any default or user-specified behaviour. 

Horizontal positioning can be adjusted by using \hfill in <cell contents>.


The <cell contents> can be almost anything.  If the tableau 
is created in math mode, the <cell contents> are processed and output 
in math mode (textstyle).  Otherwise the horizontal (non-math) mode is 
used.  Spaces before <cell contents> are ignored.  For code that
require use of alignment characters (&) or newlines (\\), group 
delimeters {...} are required.  For example: the outside braces are 
required in

   {\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}}

Group delimeters can also be used to begin the cell contents with a 
literal formatting character (e.g. {;}).  Formatting characters can 
also be disabled by redefining the \youngspecial command.


\begin{Young}...\end{Young} is provided as an alternate.

The counter {youngcounter} is incremented at the start of every 
young environment.  It is not used but the package in any other way, 
which means you can use it in any way that strikes your fancy.

--------------------------------------------------------------------
Commands that work within a cell:

The commands below have no effect if performed outside the young 
environment, but used within the environment will affect the formatting 
of the current cell.  These can be used in any combination.  Commands 
which obviously do conflicting things override each other.  Shading 
commands are ignored in a cell with no frame.  

Frame commands:
\yframe         draw cell with a frame
\ynoframe       draw cell with no frame
\ynoleft        draw cell with frame missing left side but including right
\ynoright       draw cell with frame missing right but including left
\ynoleftright   draw cell with frame missing left and right sides

Shading Commands:
\yshade[<bg>]   shade the cell in colors specified by \ysetshade
                 (or just use background color <bg>, if argument is given)
\YShade         shade the cell in colors specifide by \YSetShade
\YSHADE         shade the cell in colors specifide by \YSETSHADE
\yaltshade      shade the cell in colors specifide by \ysetaltshade
\YAltShade      shade the cell in colors specifide by \YSetAltShade
\YALTSHADE      shade the cell in colors specifide by \YSETALTSHADE

Alignment commands:
\yvalignincell{<position>} change vertical position of the cell contents

If <position> is one of {b}, {c} or {t}, the cell contents will be at 
the bottom/exact center/top of the cell (respectively).  If anything 
else is given, the default is used. (See "Environments" for more info.)

Each of the above commands has an equivalent formatting string in the 
young environment.

%%

There are five additional formatting commands which do not have equivalent
formatting strings.

\ynotop[<patch>]     don't draw the top line of the frame
\ynobottom[<patch>]  don't draw the bottom line of the frame
\ywithtop            override \ynotop
\ywithbottom         override \ynobottom
\ynoshade            don't shade the cell (overrides any shading command)

The commands \ynotop and \ynobottom are independent of the other framing
commands, and can be used together (unlike \ynoleft and \ynoright which 
override each other).  The optional argument <patch> may be used to 
manually patch the corners of the frame, if they get mangled 
(see "Bugs").  <patch> can be one of [l], [r] or [lr] (which mean patch 
left corner, patch right corner, patch both corners, respectively).  
Patching corners is only necessary when the cell is being shaded, and 
rarely even then.

Note: The combination \ynoleftright\ynotop\ynobottom behaves differently,
in a few of ways from \ynoframe.  Both create a cell with no frame;
however, the former allows the possibility of shading, and it also 
changes the default behaviour for how the next cell is drawn.  
(See "Environments")

%%

\yrighttoleft

Switches left and right.  On any single cell, a ]= frame is drawn
as a =] frame and vice versa.  If sequential cells in the same row contain 
the command \yrighttoleft, that entire sequence of cells will be reversed,
i.e. drawn from right to left, instead of left to right.  Used with 
the \yeverycell or \yeveryframe commands, it will produce something like a 
mirror image.

-------------------------------------------------------------------
Young Diagrams:

\yng[<position>][<cell size>](<r1>,<r2>,...)

This roughly mimics the \yng command from the youngtab package.  This 
command creates a young diagram with <r1> cells in the first row, <r2> 
cells in the second row, etc.  For example: \yng(4,3,1,1) creates the 
diagram of the partition (4,3,1,1).  If two or more commas appear in 
a row (blank space is ignored), a cell with no frame is drawn instead 
of starting a new row.  This feature allows us to create skew diagrams.
For example: \yng(,,3, ,,2, 4, 1) creates the diagram of (5,4,4,1)/(2,2).  

The command is implemented as a macro that creates a young environment
filled with the appropriate entries, so any defaults for the young
environment will apply here too.

--------------------------------------------------------------------
Customizing:

\ysetshade[<foreground color>]{<background color>}
\YSetShade[<foreground color>]{<background color>}
\YSETSHADE[<foreground color>]{<background color>}
\ysetaltshade[<foreground color>]{<background color>}
\YSetAltShade[<foreground color>]{<background color>}
\YSETALTSHADE[<foreground color>]{<background color>}

Set the colors used for shaded cells.  

Use of these requires the color/xcolor package to be loaded.
<background color> and <foreground color> may be any argument
that can be read by the \color command.

If arguments are left blank, defaults are used.  For example
\yshade[Blue]{} sets the foreground color to "Blue", and sets
the background color to none (default).


\ydefaultcellsize{<cell size>}

{Sets the default value for the optional argument <cell size> in
the young environment.  System default is {2.8ex}.


\ydefaultposition{<position>} 

Change sets the default value for optional argument <position> in
the young environment.  It's not obvious to me what the right system
default should be here.  For better or for worse, it's {b}.


\yhwratio{<height>:<width>}

Sets the height to width ratio of the cells. <height> and <width> must
be positive integers.  System default is {1:1}. 


\renewcommand{\youngspecial}{<characters>} 

Sets the list of characters that are processed as "special formatting
characters" in a tableau entry.  The system default is {,;=!?^_}.  
For example: \renewcommand{\youngspecial}{,;=^_} disables ! and ? 
as formatting characters, and instead the young environment treats ! and ? 
as literal characters.  In this case the shading features can still be 
accessed though the commands \yshade etc.  Note: brackets are not 
considered special characters, since they must be used in combination 
with other formatting charcters to produce formatting effects.


\yeverycell{<command sequence>}

Inserts <command sequence> at the beginning of every cell.  <command sequence> 
is processed before the rest of the cell entry is read, including any 
formatting strings.  This means any cell formatting commands in
<command sequence> can be overrridden on a case-by-case basis.  
For example, \yeverycell{\yshade} will shade every cell in 
the colors set by \ysetshade, unless another shading option is specified.


\yeveryframe{<command sequence>}

Like \yeverycell, except: (1) <command sequence> is inserted at the
end of the cell, not at the beginning, thus formatting commands in 
<command sequence> cannot be overridden.  (2)  <command sequence> is only 
inserted on cells with frames.  This may be the less useful of the two,
however if you insert a clever function, it can be used to make the 
\yng command automatically produce tableaux.  (See "Example".)



\setlength{\ybaselineoffset}{<depth>}

Specifies where the baseline is relative to the center of the cell.
Specifically, the baseline is \ybaselineoffset below the center of
the cell. The default is .75ex, which is approximately half the font 
size.


\setlength{\yframethickness}{<thickness>}

Sets the thickness of the cell frames.  If <thickness> is 0pt, the frames
will be invisible.  Default is 0.5pt.


\setlength{\yautosizeminimun}{<size>}

The smallest box size allowed by the autosizing mechanism.


\setlength{\ycellpadding}{<length>}

The algorithms for vertical positioning and autosizing always try
pad the cell contents with at least this much space.  Default is
0.3ex.


Note: the effects of any of these commands are local--if used within
a group, the effects are restricted to the group.

--------------------------------------------------------------------
Autosizing:

Autosizing, like LaTeX referencing, is done via a two pass mechanism.
The main reason for this is that I don't know how to to make TeX 
calculate how big the cells should be before drawing them.  So, instead, 
the size is calculated as the tableau is drawn, and written to the .aux 
file.  The next time LaTeX is run, the data from the .aux file are used 
to determine the sizes of the boxes.  

The downside is that you may need to run LaTeX twice to get autosizing 
to work properly.  A warning message will tell you if another pass
is needed.

The upside is that this mechanism makes it is possible to autosize two 
or more tableaux to have exactly the same size.  To do this, use the syntax 

\begin{young}[auto=<label>]  ... \end{young}.  

Any two tableaux with the same <label> will automatically have the same 
cell size.

--------------------------------------------------------------------
Backwards Compatibility:

For the most part, there should be few backwards compatibility issues,
with the origial "young" package.  However, the addition of two optional 
arguments, and the treatment of certain characters as formatting 
information do have the potential to cause some compatibility issues.  
These are easily resolved by including offending material in braces.

If better backwards compatibility is desired, it can be attained 
by changing defaults.  For example the following code effectively 
recreates the Young environment from the original package.

\renewenvironment{Young}{% redefine Young environment to use original defaults
  \hbox\bgroup%        never use math mode for entries
  \def\youngspecial{}% disable formatting characters
  \yhwratio{12:13}% set height to width ratio
  \setlength{\ybaselineoffset}{3.6pt}% set baseline position
  \setlength{\ycellpadding}{0pt}%  don't try to pad the entries with space
  \begin{young}[12pt][bb]% now start the young environment with these argument
}%
{\end{young}\egroup}% end of redefinition

--------------------------------------------------------------------
Bugs (and other quirks):

Shading a cell overwrites part of half of the frames of the cells 
above and to its left.  This is done intentionally---it works well
most of the time---but has a downside: you need to be careful about
drawing frames of shaded boxes.  For example, with
    \begin{young}
    =]!1 & ==!2
    \end{young}
you'll see that the frame center line is only half as thick as it
should be.  The solution is to use
    \begin{young}
    =]!1 & ]=!2
    \end{young}
instead.  Similar issues arise when using \ynotop and \ynobottom,
which is why these have an optional <patch> argument.  To avoid
these issues, one would need to keep track of all the different
frames that have been drawn, which is something I'm not willing to 
try to do in TeX.

Sometimes autosizing generates a warning to rerun LaTeX, when it
isn't actually necessary to do so.  This is only a minor nuissance,
since you should never get an _unnecessary_ warning if LaTeX is run 
twice in a row on the same input file.  Any warnings generated on
the second run should be taken seriously.  It should not be possible
(or at least not easy!) to get a false negative---a situation where 
a warning to rerun should be generated, but isn't.

The environment doesn't do any checking for invalid input, which
may lead to impenetrable error messages or strange behaviour if 
invalid input is given.  For example, if invalid optional arguments 
are provided to the young environment, two things could happen:
options are ignored, or an error results.  It's not very consistent.

There is no good reason for insisting that the formatting characters
be given in the order <frame><shading><alignment>, except that it
is harder to implement their parsing in arbitrary order.

The young environment can't create a row with zero cells, so the 
command \yng(2,1,0), actually creates an unframed cell in the third
row (and the corresponding horizontal space).  The extra space isn't
actually a problem, unless you do something like \yng(0,0,0)....
Here's the actual bug: Normally these are empty---however if \yeverycell 
has declared some interesting behaviour, they may not be.  An easy 
pseudo-fix would be to not draw contents of the cell, but this conceals 
the fact that the contents are actually read and processed nevertheless... 
which (if it made a difference) would be an even more perplexing bug.  
The solution (for now), is to use \yeveryframe instead in this situation.

There is no extra space around a tableau.

There must be something other than empty space in the young environment 
in order to create a tableau.  For example: \begin{young} \end{young}
and \begin{young}\empty\end{young} do produce any output.  However, 
\begin{young}\relax\end{young}, or \begin{young}\\\end{young} will 
create a single empty box.

There are probably other bugs that I don't know about.  This has
not been exhaustively tested.

--------------------------------------------------------------------
Example:

\documentclass{article}
\usepackage{young}
\usepackage[svgnames]{xcolor}

%
% set some default colors
%
\ysetshade{Green!15}%      a pale green
\YSetShade{Green!50}%      slightly darker green
\ysetaltshade{Blue!15}%    a pale blue
\YSetAltShade{Blue!50}%    a slightly darker blue

\begin{document}

% 
% A basic example of a skew tableau.  The comma creates a cell with
% no frame.
\noindent
A skew tableau:

\begin{young}            
, & , & , & 3 & 5 & 10\\
, & 1 & 4 & 6 \\
2 & 7 & 8  \\
9 & 11  
\end{young}

%
% If we just want unfilled boxes, the \yng command can be used.
% The extra commas create unframed cells instead of new rows.
%
\bigskip \noindent
A young diagram  and a skew diagram.

\yng(5,5,4,2) \qquad \yng(,,3,,3,4,2)

%
% The next example illustrates shading with the default colors.
% The formatting strings ! and ? use the colors set by \ysetshade
% and \yaltshade respectively.  !! and ?? use the colors set by 
% \YSetShade and \YAltShade.  !!! and ??? are also valid, but
% not illustrated in this example.
%
\bigskip \noindent
Shading with two default colors:

\begin{young}
,  & ,  & !1 & !2 & ?5 & ?6 \\
!3 & !5 & !6 & ?1  \\
!4 & ?2 & ?3 & ?4  
\end{young}

\bigskip \noindent
Same example with some highlighted boxes:

\begin{young}
,  & ,  & !1 & !2 & ?5 & ?6 \\
!3 & !5 &!!6 &??1  \\
!4 & ?2 & ?3 & ?4 
\end{young}

%
% The next example illustrates use of the optional arguments.  One
% argument is position, the other is cell size.  They can be given
% in either order.  The use of [tt] as the position makes the top
% of the cells of the two tableaux line up, even though they are the
% different sizes---however, this probably not the option you want
% to use most of the time.  The second example uses autosizing, 
%
\bigskip \noindent
Some tableaux with different sized cells.  If the one on the right 
looks weird, you need to rerun LaTeX.

\begin{young}[30pt][tt]
cell & size & is \\    
30pt & here
\end{young}
%
\qquad
%
\begin{young}[tt][auto]
here it's & autosize
\end{young}

%
% The next example illustrates the use of formatting instructions to
% make tabloids. In the first example, the ]= instructs the environment 
% to create a cell missing the right side of the frame.  From then on
% the default behaviour creates the rest of the frames the way we want,
% so no further formatting instructions are needed.  In the second 
% example the == instructure creates a cell missing the right and left 
% sides of the frame.  Again, the default behaviour does the right 
% thing from then on.
%
\bigskip \noindent
Tabloid variants:

\begin{young}     
]=3 & 4 & 8 & 9 \\
1 & 5 & 6 \\
2 \\
7 
\end{young}
%
\qquad
%
\begin{young}
==3 & 4 & 8 & 9 \\
1 & 5 & 6 \\
2 \\
7 
\end{young}

%
% Illustration of the optional argument to the ! instruction.
%
\bigskip \noindent
Just some colored boxes:

\begin{young}
, & ![Orange] & ![Red] \\
![Yellow] & ![Blue] \\
![Green] & ![Purple] 
\end{young}

%
% Just for fun, an illustration of the \yeveryframe command.  Here the 
% value of a counter is automatically inserted into every cell with a 
% frame, which allows us to produce superstandard tableaux using 
% the \yng command.
%
\bigskip \noindent
Automatically generated superstandard tableaux:

\newcounter{superstd}[youngcounter]
{
  \yeveryframe{\stepcounter{superstd}\thesuperstd}
  \yng(10,5,2,1) \qquad \yng(,,,7, ,4,2,1)
}

\bigskip \noindent
We can also number from right to left:

{
  \yeveryframe{\stepcounter{superstd}\thesuperstd\yrighttoleft}
  \yng(10,5,2,1) \qquad \yng(,,,7, ,4,2,1)
}

\end{document}