### Abstract

Given a linear recurrence integer sequence U = {u_{n}}, u_{n+2} = u_{n+1} + u_{r}, n ≥ 1, u_{1} = 1, u_{2}> u_{1}, 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 |
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Pages (from-to) | 201-211 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 22 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1978 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*22*(3), 201-211. https://doi.org/10.1016/0012-365X(78)90053-5

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

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 22, no. 3, pp. 201-211. https://doi.org/10.1016/0012-365X(78)90053-5

}

TY - JOUR

T1 - On additive partitions of integers

AU - Alladi, K.

AU - Erdős, P.

AU - Hoggatt, V. E.

PY - 1978

Y1 - 1978

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0142193777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142193777&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(78)90053-5

DO - 10.1016/0012-365X(78)90053-5

M3 - Article

AN - SCOPUS:0142193777

VL - 22

SP - 201

EP - 211

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 3

ER -