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Packing Ferrers Shapes

Published online by Cambridge University Press:  01 May 2000

NOGA ALON ,
MIKLÓS BÓNA  and
JOEL SPENCER
NOGA ALON
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA, and Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel (e-mail: noga@math.tau.ac.il)
MIKLÓS BÓNA
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA (e-mail: bona@math.ias.edu)
JOEL SPENCER
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA, and Department of Mathematics and Computer Science, Courant Institute, NYU, NY 10012, USA (e-mail: spencer@cs.nyu.edu)
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Abstract

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Answering a question of Wilf, we show that, if n is sufficiently large, then one cannot cover an n × 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 Θ(p(n)/log n):

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 9 , Issue 3 , May 2000 , pp. 205 - 211
Copyright
2000 Cambridge University Press