We will identify the shifted staircase of size n with its shifted Ferrers diagram as shown in Figure 1.
We define the truncated shape [lambda]\[mu] to be the diagram obtained from the Ferrers diagram of [lambda] by removing the [[mu].
We will also denote by [lambda] the Ferrers diagram
associated with the partition [lambda].
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.
Equivalently, we have that [lambda] [subset or equal to] [mu] if and only if the Ferrers diagram
of [lambda] fits inside the Ferrers diagram
Represent a partition [lambda] by its Ferrers diagram
in the English notation, which is an array of [[lambda].
: A Ferrers diagram
F is a left aligned finite set of unit cells in [Z.
A partition A is classically represented by a Ferrers diagram
Keywords: plane partition, partition, Ferrers diagram
, limit law, combinatorial probability
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
de Mier, k-noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams
, Combinatorica 27 (2007), 699-720.