Arrays and the combinatorics of Young tableaux

The classical theory of Young tableaux is presented in the rather new and non-traditional language of arrays. With the usual operations (or algorithms) of insertion and jeu de taquin as a starting point, more elementary operations on arrays are introduced. The set of arrays equipped with these operations forms an object which can be referred to as a bicrystal. This formalism is presented in the first part of the paper, and its exposition is based on the theorem that the vertical and horizontal operators commute. In the second part the apparatus of arrays is used to present some topics in the theory of Young tableaux, namely, the plactic monoid, Littlewood–Richardson rule, Robinson–Schensted–Knuth correspondence, dual tableaux, plane partitions, and so on.