Packing Ferrers Shapes

DOI10.1017/S0963548300004223zbMATH Open0955.05025arXivmath/9812075MaRDI QIDQ4500419

Noga Alon, Miklós Bóna, Joel Spencer

Publication date: 12 February 2001

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Abstract: Answering a question of Wilf, we show that if $n$ is sufficiently large, then one cannot cover an $nimesp(n)$ 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 $Theta(p(n)/logn).$

Full work available at URL: https://arxiv.org/abs/math/9812075

zbMATH Keywords

integer partitionFerrers diagramtiling a rectangleFerrers shape

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Combinatorial aspects of tessellation and tiling problems (05B45) Combinatorial aspects of packing and covering (05B40)

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