We will identify the shifted staircase of size n with its shifted Ferrers diagram as shown in Figure 1.

For two partitions [lambda] = ([[lambda].sub.1], ..., [[lambda].sub.k]) and [mu] = ([[mu].sub.l], ..., [[mu].sub.l]), the usual skew shape [lambda]/[mu] is defined to be the set-theoretic difference [lambda] - [mu] of their Ferrers diagrams. We define the truncated shape [lambda]\[mu] to be the diagram obtained from the Ferrers diagram of [lambda] by removing the [[mu].sub.i] cells from the left in the (k + 1 - i)th row for i = 1, 2, ..., 1.

A partition [lambda] = ([[lambda].sub.1], ..., [[lambda].sub.k]) can be represented by its

Ferrers diagram, which is obtained by drawing k rows of contiguous unit cells, from top to bottom, such that row i contains [[lambda].sub.i] cells, and with the first cells of these k rows vertically aligned.

A convenient way to visualize a partition [lambda] = ([[lambda].sub.1], [[lambda].sub.2], ..., [[lambda].sub.m]) is to consider its

Ferrers diagram (denoted by [[lambda]]), which is composed of cells organized in left-justified rows such that the i-th row (from bottom to top) contains A, cells.

The

Ferrers diagram of [lambda] consists of [[lambda].sub.i] left justified boxes in the ith row from the top ('English notation').

Represent a partition [lambda] by its

Ferrers diagram in the English notation, which is an array of [[lambda].sub.i] boxes in row i, with the boxes justified upwards and to the left.

Ferrers diagrams: A

Ferrers diagram F is a left aligned finite set of unit cells in [Z.sup.2], in decreasing number from top to bottom, considered up to translation: see Figure 1, left.

A partition A is classically represented by a

Ferrers diagram,

Keywords: plane partition, partition,

Ferrers diagram, limit law, combinatorial probability

Definition 3.7 A James-Peel tree T for D is complete if its leaves [A.sub.1], ..., [A.sub.n] are equivalent to

Ferrers diagrams of partitions and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

k-noncrossing and k-nonnesting graphs and fillings of

Ferrers diagrams. Combinatorica, 27(6):699-720, 2007.

de Mier, k-noncrossing and k-nonnesting graphs and fillings of

Ferrers diagrams, Combinatorica 27 (2007), 699-720.