Parallelepipeds in sets of integers

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Abstract

A d-dimensional parallelepiped in N is a set of the form {m + ∑i ε{lunate} Smi: S ⊆ {1, 2,..., d}} for some positive integers m, m1, m2,..., md. It is proved that a subset of {1, 2,..., N} not containing a d-dimensional parallelepiped is of cardinality not exceeding N1 - 1 2d - 1 + O(N 3 4 - 1 2d - 1). A result of a similar nature is established for parallelepipeds satisfying m1|m2| ... | md.

Original languageEnglish
Pages (from-to)163-170
Number of pages8
JournalJournal of Combinatorial Theory - Series A
Volume45
Issue number2
DOIs
StatePublished - 1 Jan 1987

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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