How many atoms can be defined by boxes?

Research output: Contribution to journalArticle

2 Citations (Scopus)


We study the function b(n, d), the maximal number of atoms defined by n d-dimensional boxes, i.e. parallelopipeds in the d-dimensional Euclidean space with sides parallel to the coordinate axes. We characterize extremal interval families defining b(n, 1)=2 n-1 atoms and we show that b(n, 2)=2 n 2-6 n+7. We prove that for every d, {Mathematical expression} exists and {Mathematical expression}. Moreover, we obtain b*(3)=8/9.

Original languageEnglish
Pages (from-to)193-204
Number of pages12
Issue number3
Publication statusPublished - Sep 1 1985


  • AMS subject classification (1980): 51M05, 52A20

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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