Drawing Young tabloids

Question

I would like LaTeX to produce output like the following

(without the 2 a so called Young tabloid), ideally by writing

\ytabloidshort{123,56}

(using one character per cell, ideally allowing groups via brackets as in \ytabloidshort{89{10}{\ldots}{n+1},56}, but that is not important, the following is sufficient) or

\begin{ytabloid}
1 & 2 & 3 \\
4 & 5
\end{ytabloid}

of course with arbitrarily many rows and columns. The command/environment must (also or only) work in mathmode. That's why I included the 2 \cdot in the following examples.

I have found several ways to generate output similar to the desired, but they are all unacceptable.

\documentclass{article}

\usepackage{amsmath}
\usepackage{booktabs}
\usepackage{ytableau}
\usepackage{tikz}
\usetikzlibrary{matrix}

\begin{document}

perfect, but I do not see a way to remove the vertical lines while keeping the 
horizontal ones (ytableau):
\[ 2 \cdot
\ytableausetup{centertableaux}
\begin{ytableau}
1 & 2 & 3 \\
4 & 5
\end{ytableau}
\]

matrix (amsmath) and cline:
\[ 2 \cdot
\begin{matrix}
\hline
1 & 2 & 3 \\ \hline
4 & 5 \\ \cline{1-2}
\end{matrix}
\]

matrix (amsmath) and cmidrule (booktabs):
\[ 2 \cdot
\cmidrulewidth=\lightrulewidth
\begin{matrix}
\midrule
1 & 2 & 3 \\ \midrule
4 & 5 \\ \cmidrule{1-2}
\end{matrix}
\]

tikzpicture and matrix (TikZ/PGF with library matrix):
\[ 2 \cdot
\begin{tikzpicture}
\matrix[matrix of math nodes] (m) {
1&2&3\\
4&5\\
};
\draw (m-1-1.north west) -- (m-1-3.north east);
\draw (m-1-1.south west) -- (m-1-2.south east);
\draw[red] (m-2-2.north west) -- (m-2-2.north east); % shows that lines don't overlap
\draw (m-2-1.south west) -- (m-2-2.south east);
\end{tikzpicture}
\]

\end{document}

Two (and more) disadvantages remain:

• The output is ugly, actually unusable.
• They are all very uncomfortable to write.

What do you suggest?

Is it, for example, possible to parse the argument of \ytabloidshort and draw a matrix, each cell with content automatically with a line above and below. (But note the "problem in red"). How would one implement such a \newcommand? Any other ideas are also welcome.

I can split this problem into three questions:

1. How do I get tabloids whose appearance fits to tableaux generated with the package ytableau?
2. How can I make the result of (1.) work in connection with other maths, cf. the 2 \cdot?
3. How can I generate (1.) in a comfortable way?

Solutions so far:

Ryan extented his package ytableau to draw tabloids. As long as your are using the package, this solves all three questions. The picture above can be generated by

\usepackage{ytableau} % version 1.3 or higher

\ytableausetup{tabloids, centertableaux}
\[ 2 \cdot \ytableaushort{123,45} \]

Sticking to the questions the status is the following.

1. Actually none. Spacing must be adapted.
2. Actually none. Alignment and spacing must be adapted.
3. Scott showed a way to generate the desired matrix by a makro. This is definitely worth noting and may be helpful in many other situations.

Answer 1

I've expanded ytableau a little to include an option to draw tabloids.

\documentclass{standalone}
\usepackage{ytableau}
\begin{document}
  \ytableausetup{tabloids,centertableaux}
  $2\cdot\ytableaushort{123,45,6}$
\end{document}

Currently the new version is on my website and has also been uploaded to CTAN.

Answer 2

The ytableau package (by Ryan Reich) could be an option (examples take almost verbatim from the package documentation):

\documentclass{article}
\usepackage{amsmath}
\usepackage{ytableau}

\begin{document}

\ytableausetup{textmode}
\begin{ytableau}
a & d & f \\
b & e & g \\
c
\end{ytableau}

\ytableausetup{mathmode}
\begin{ytableau}
a & d & \ldots & f \\
b & e
\end{ytableau}

\[
\ytableausetup
{boxsize=1.25em}
\ytableausetup
{aligntableaux=top}
\ytableaushort[x_]{135,24,6}
+ \ydiagram[*(red!20) ]{3} \\
+ \ydiagram[*(blue!20)]{3,2,1}
= \ytableaushort[x_]{135,24,6}
*[*(red!20)]{3} *[*(blue!20)]{3,2,1}
\]

\end{document}

CTAN mentions two other packages associated to Young tabloids: youngtab and young, but ytableau is the most flexible and customizable one, as far as I could see.

If you don't like the rules, you can suppress them by saying

\makeatletter
\def\boxframe@YT{0.0em}
\makeatother

in the preamble.

Answer 3

Here's an option. I'm not sure why you don't like the booktabs + matrix option, so you may not like this as well. However, it should give you an idea of how it can be implemented.

Edit 1: I removed a hardcoded value and added some of the booktabs constants into the function, you could fiddle with those to achieve spacing/weight that you like.

Edit 2: The case suggested in your comment should work now. This still requires the first row to be the longest however.

Edit 3: Removed hardcoded displayed math environment because, well, it was a bad idea.

\documentclass{article}
\usepackage{xparse}
\usepackage{booktabs}
\ExplSyntaxOn
\tl_new:N \l_my_body_tl
\int_new:N \l_first_row_count_int
\int_new:N \l_row_count_int
\int_set:Nn \l_row_count_int {1}
\cs_new:Npn \make_tab_row:n #1
    {
        \tl_clear:N \l_tmpa_tl
        \int_compare:nTF { \l_row_count_int = 1 }
          {
            \int_set:Nn \l_first_row_count_int {\tl_count:n {#1}}
            \int_set:Nn \l_tmpa_int {\tl_count:n {#1}}
          }
          {
            \int_set:Nn \l_tmpa_int {\tl_count:n {#1}}
          }
        \tl_set:Nx \l_tmpb_tl {\clist_item:Nn \g_tmpa_clist {\l_row_count_int + 1}}
        \int_set:Nn \l_tmpb_int {\tl_count:N \l_tmpb_tl}
        \int_set:Nn \l_tmpa_int {\int_max:nn \l_tmpb_int \l_tmpa_int}

        \tl_map_inline:nn {#1} {\tl_put_right:Nn \l_tmpa_tl {& ##1}}
        \tl_put_right:Nn \l_tmpa_tl {\\\cmidrule}
        \tl_put_right:Nx \l_tmpa_tl {{1-\int_to_arabic:n \l_tmpa_int}}
        \tl_set:Nx \l_tmpa_tl { \tl_tail:N \l_tmpa_tl }
        \tl_put_right:NV \l_my_body_tl \l_tmpa_tl
        \int_incr:N \l_row_count_int
    }

\NewDocumentCommand {\tabloidshort} { m }
    {
        \heavyrulewidth=.08em
        \cmidrulewidth=.08em
        \belowrulesep=.65ex
        \aboverulesep=.4ex
        \clist_gset:Nn \g_tmpa_clist {#1}
        \clist_map_function:nN { #1 } \make_tab_row:n
         \begin{array}{*{\int_use:N \l_first_row_count_int}{c}}
            \toprule
            \tl_use:N \l_my_body_tl
        \end{array}
        \tl_clear:N \l_my_body_tl
        \int_zero:N \l_first_row_count_int
        \int_set:Nn \l_row_count_int {1}
    }
\ExplSyntaxOff


\begin{document}

$\tabloidshort{12{10}5,1{\cdots}3,12}$

\[
\tabloidshort{89{10}{\ldots}{n+1},56}
\]

\begin{equation}
\tabloidshort{123,4,5,67}
\end{equation}

\end{document}

Answer 4

This was actually an exercise for me to learn xstring and etoolbox functions a little bit better so the end result is not polished and there is no optimization of any sort. Also there is a space on the left side when used inline. I can't see why.

The syntax is simply a comma seperated list which should be terminated by an additional comma otherwise the last entry is omitted.

\documentclass[12pt]{article}
\usepackage{xstring,tikz,etoolbox}
\usetikzlibrary{matrix}
\newcommand{\youngtab}[1]{%
\def\youngrowlist{#1}%
    \StrCount{\youngrowlist}{,}[\rownum]%
    \foreach \x in {1,...,\rownum}{%
        \StrBefore{\youngrowlist}{,}[\mynextrow]%
        \StrLen{\mynextrow}[\numlength]%
        \csxdef{rowlen\x}{\numlength}%
        \csxdef{row\x}{\mynextrow}%
        \StrGobbleLeft{\youngrowlist}{\number\numexpr\numlength+1\relax}[\mytemplist]%
        \xdef\youngrowlist{\mytemplist}%
        \let\mytemplist\empty%
        \csgdef{rowconcat\x}{}%
        \foreach \y in {1,...,\numlength}{%
            \StrChar{\csuse{row\x}}{\y}[\nextdigi]%
            \edef\mytemplist{\csuse{rowconcat\x}\nextdigi\relax}%
            \csxdef{rowconcat\x}{\mytemplist\&\relax}%
        }
    }
    \foreach \x in {1,...,\rownum}{
     \begingroup\edef\pfff{\endgroup%
         \noexpand\gappto\noexpand\mymatrixcontent{\csuse{rowconcat\x}\noexpand\\}}\pfff
    }%
    \tikz[baseline=(m.center)] {\matrix (m) [matrix of math nodes,ampersand replacement=\&] {\mymatrixcontent};
    \draw \foreach \x in {1,...,\rownum}{(m.west |- m-\x-1.south west) -- (m-\x-\csuse{rowlen\x}.south east)};
    \draw (m.west |- m-1-1.north west) -- (m-1-\csuse{rowlen1}.north east |- {{m.west |- m-1-1.north west}});}%
    \let\mymatrixcontent\empty
    \let\youngrowlist\empty
}

\begin{document}
Spelling tableau \youngtab{789c,a3\%,45687,r,} correctly is very difficult so we populate this line with wise 
words to see the vertical placement. Then an equation follows: 
\begin{equation}
2\cdot \youngtab{1453,{\cdots}4,45687,6,68,}
\end{equation}
The rows are drawn but should it follow the the upper and the lower rows if they are longer, I don't know yet. 
\end{document}

However, I think a pgfplotstable solution that is working inside a macro, should also be considered.