Jeu de taquin
Jeu de taquin (literally: teasing or annoying game) is the French name for the 15 puzzles or 15 puzzles .
In the field of combinatorics , a construction according to Marcel Schützenberger is called jeu de taquin , which defines an equivalence relation on the set of Schief standard Young tableaux . A jeu-de-taquin-slide is a transformation that shifts the numbers in a tableau similar to a 15 puzzle. Two tableaus are jeu-de-taquin-equivalent if and only if one can be converted into the other by virtue of a sequence of such shifts.
Definition of a jeu-de-taquins
A Schief standard Young tableau T of the form is given . Choose an adjacent empty cell c, which can be added to it, that means that c must have at least one edge in common with a cell from T and also together with form a slate table again. There are two ways to perform shifts, depending on whether c top left or bottom right of T is. Let us assume the former. Then we shift the number of its neighboring cell to c; if c has a number as neighbors on both the left and right, then we choose the smallest of the two, if not, then the shift is complete. The tableau that we get after this transformation is again a Schief-Young tableau.
