Packing Ferrers Shapes

Details Packing Ferrers Shapes Packing Ferrers Shapes

1998-12-11

arxiv.org/abs/math/9812075v1

Mathematics

Combinatorics

7 pages, 4 figures

Scientific paper

Answering a question of Wilf, we show that if $n$ is sufficiently large, then
one cannot cover an $n \times p(n)$ rectangle using each of the $p(n)$ distinct
Ferrers shapes of size $n$ exactly once. Moreover, the maximum number of
pairwise distinct, non-overlapping Ferrers shapes that can be packed in such a
rectangle is only $\Theta(p(n)/ \log n).$

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