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time a rook is placed i new rows are created and drawn to the right end and immediately
above where we placed the rook. For i>0, as we place a rook, the next rook to be placed
has an increased number of possible positions. Note that i = 0 corresponds to the classical
rook placements considered in preceding sections.
Example 2.63 Let us consider the Ferrers board B(1, 1, 3, 3, 5) shown in Figure 2.3. We
will place 3 non-taking rooks in columns 1, 3,and4 using a 1-creation rule. For the first
rook in the first column, there is only one possibility to place it. After placing the rook, we
create to the right of the rook a new row. The result ...