Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T21:50:26.738Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)