# On additive partitions of integers

K. Alladi, P. Erdős, V. E. Hoggatt

Research output: Contribution to journalArticle

9 Citations (Scopus)

### 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 language English 201-211 11 Discrete Mathematics 22 3 https://doi.org/10.1016/0012-365X(78)90053-5 Published - 1978

### Fingerprint

Partition
Integer Sequences
Linear Recurrence
Integer
Disjoint
Distinct
Subset
Graph in graph theory
Generalization
Interpretation

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

On additive partitions of integers. / Alladi, K.; Erdős, P.; Hoggatt, V. E.

In: Discrete Mathematics, Vol. 22, No. 3, 1978, p. 201-211.

Research output: Contribution to journalArticle

Alladi, K. ; Erdős, P. ; Hoggatt, V. E. / On additive partitions of integers. In: Discrete Mathematics. 1978 ; Vol. 22, No. 3. pp. 201-211.
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