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.
: 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.