Ferrers Diagram
A Ferrers diagram represents partitions as patterns of dots, with the 
th row having the same number of dots
as the 
th term in the partition.
The spelling "Ferrars" (Skiena 1990, pp. 53 and 78) is sometimes also
used, and the diagram is sometimes called a graphical representation or Ferrers graph
(Andrews 1998, p. 6). A Ferrers diagram of the partition
 |
for a list 
, 
, ..., 
of 
positive
integers with 
is therefore the
arrangement of 
dots or square boxes in 
rows, such that
the dots or boxes are left-justified, the first row is of length 
, the second row
is of length 
, and so on, with the 
th row of length
. The above diagram corresponds to one of the possible
partitions of 100.
The partitions of integers less than or equal to 
in which there
are at most 
parts and in which no part is larger
than 
correspond (1) to Young tableaux which
fit inside an 
rectangle and (2) to lattice
paths which travel from the upper right corner of the rectangle to the lower left
in 
leftward and downward steps. The number
of Young diagrams fitting inside an 
rectangle
is given by the binomial coefficient 
. The above example shows the
 |
Young 
diagrams.
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