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I would like to draw border strip tableaux in Latex. Such a tableau is a tiling of a partition shape (or skew-partition shaped) diagram with labeled border strips such that in each row and column, the labels are increasing. For a precise definition, see page 351 in

http://www-math.mit.edu/~rstan/pubs/pubfiles/123.pdf

In the picture, all the border strips are of the same length. This special case is enough for my purposes but does not hold in general.

The picture is copied from Figure 2.4 in http://www.ams.org/journals/tran/2000-352-12/S0002-9947-00-02666-0/S0002-9947-00-02666-0.pdf

You mean like this (this includes @CarLaTeX's suggestion to use arraystretch):

documentclass[border=3.14mm]{standalone}

usepackage{array}

renewcommand{arraystretch}{1.4}

begin{document}

    begin{tabular}{|lllllllll}

        hline

        multicolumn{3}{|c|}{1}                                                  & multicolumn{1}{l|}{}  & 5                     & multicolumn{1}{l|}{}   & multicolumn{1}{l|}{}   & 13                    & multicolumn{1}{l|}{} \ cline{1-3} cline{6-6} cline{9-9} 

        2                      & multicolumn{1}{l|}{}  &                        & multicolumn{1}{l|}{4} & multicolumn{1}{l|}{} &                         & multicolumn{1}{l|}{8}  & multicolumn{1}{l|}{} &                       \ cline{2-8}

        multicolumn{1}{|l|}{} & multicolumn{1}{l|}{}  & multicolumn{1}{l|}{}  & 9                      & multicolumn{1}{l|}{} & multicolumn{1}{l|}{}   & multicolumn{1}{l|}{}   &                       &                       \ cline{1-1} cline{5-5}

        & multicolumn{1}{l|}{3} & multicolumn{1}{l|}{7} & multicolumn{1}{l|}{}  &                       & multicolumn{1}{l|}{10} & multicolumn{1}{l|}{12} &                       &                       \ cline{1-2} cline{4-6}

        6                      & multicolumn{1}{l|}{}  & multicolumn{1}{l|}{}  &                        & 11                    & multicolumn{1}{l|}{}   & multicolumn{1}{l|}{}   &                       &                       \ cline{2-7}

        multicolumn{1}{|l|}{} &                        & 14                     & multicolumn{1}{l|}{}  &                       &                         &                         &                       &                       \ cline{1-4}

    end{tabular}

end{document}

which will give you:

Since this can be easily achieved by tabular environment, I have directly utilized it.

PS: In case, if you have something else in mind, please consider giving an MWE.

Disclaimer: I specifically chose not to use tikz here. Instead, I used tabular -- though it does not match the tags of the question -- only because it is elegant for this class of typesetting ;).

A variation on the theme of Raaja's answer, who the credit should go. The advantage here is a more readable syntax, where each cell is specified (the optional argument is the contents, if not empty).

documentclass{article}

usepackage{array,xparse}



NewExpandableDocumentCommand{?}{O{}m}{%

  multicolumn{1}{#2}{makebox[0.6em]{#1}}%

}



begin{document}



[

renewcommand{arraystretch}{1.4}

begin{tabular}{*{9}{c}}

hline

?{|c}    & ?[1]{c}  & ?{c|}    & ?{c|}    & ?[5]{c}  & ?{c|}     & ?{c|}    & ?[13]{c} & ?{c|} \

cline{1-3} cline{6-6} cline{9-9}

?[2]{|c} & ?{c|}    & ?{c}     & ?[4]{c|} & ?{c|}    & ?{c}      & ?[8]{c|} & ?{c|} \

cline{2-8}

?{|c|}   & ?{c|}    & ?{c|}    & ?[9]{c}  & ?{c|}    & ?{c|}     & ?{c|} \

cline{1-1} cline{5-5}

?{|c}    & ?[3]{c|} & ?[7]{c|} & ?{c|}    & ?{c}     & ?[10]{c|} & ?[12]{c|} \

cline{1-2} cline{4-6}

?[6]{|c} & ?{c|}    & ?{c|}    & ?{c}     & ?[11]{c} & ?{c|}     & ?{c|} \

cline{2-7}

?{|c|}   & ?{c}     & ?[14]{c} & ?{c|} \

cline{1-4}

end{tabular}

]



end{document}