On additive partitions of integers

K. Alladi, P. Erdös, V. E. Hoggatt

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Abstract

Given a linear recurrence integer sequence U = {un}, un+2 = un+1 + ur, n ≥ 1, u1 = 1, u2> u1, we prove that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U. We give a graph theoretic interpretation of this result, study related problems and discuss possible generalizations.

Original languageEnglish
Pages (from-to)201-211
Number of pages11
JournalDiscrete Mathematics
Volume22
Issue number3
DOIs
Publication statusPublished - 1978

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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