These changes may seem arbitrary, but they actually make the "only reasonable choices"—meaning the only choices that keep the columns of the tableau (disregarding the empty cell) strictly increasing (as opposed to just weakly increasing). Rectification Given a skew standard or skew semistandard tableau T, one can iteratively apply inward slides to T until the tableau becomes straight-shape (which means no more inward slides are possible). This can generally be done in many different ways (one can freely choose into which cell to slide first), but the resulting straight-shape tableau is known to be the same for all possible choices. This tableau is called the rectification of T. Jeu-de-taquin equivalence Two skew semistandard tableaux T and S are said to be jeu-de-taquin equivalent if one can transform one of them into the other using a sequence (possibly empty) of slides (both inward and outward slides being allowed). Equivalently, two skew semistandard tableaux T and S are jeu-de-taquin equivalent if and only if they have the same rectification. Reading words and Knuth equivalence There are various ways to associate a word (in the sense of combinatorics, i. e., a finite sequence of elements of an alphabet—here the set of positive integers) to every Young tableau. We choose the one apparently most popular: We associate to every Young tableau T the word obtained by concatenating the rows of T from the bottom row to the top row. (Each row of T is seen as a word simply by reading its entries from left to right, and we draw Young tableaux in English notation so that the longest row of a straight-shape tableau appears at the top.) This word will be referred to as the reading word, or briefly as the word, of T. It can then be shown that two skew semistandard tableaux T and S are jeu-de-taquin equivalent if and only if the reading words of T and S are Knuth equivalent. As a consequence, the rectification of a skew semistandard tableau T can also be obtained as the insertion tableau of the reading word of T under the Robinson-Schensted correspondence. The Schützenberger involution Jeu de taquin can be used to define an operation on standard Young tableaux of any given shape, which turns out to be an involution, although this is not obvious from the definition. One starts by emptying the square in the top-left corner, turning the tableau into