### Abstract

We consider a partition of the subsets of the natural numbers ℕ into two classes, the lower class and the upper class, according to whether the representation function of such a subset A, counting the number of pairs of elements of A whose sum is equal to a given integer, is bounded or unbounded. We give sufficient criteria for two subsets of ℕ to be in the same class and for a subset to be in the lower class or in the upper class.

Original language | English (US) |
---|---|

Title of host publication | Combinatorial and Additive Number Theory - CANT 2011 and 2012 |

Editors | Melvyn B. Nathanson |

Publisher | Springer New York LLC |

Pages | 43-53 |

Number of pages | 11 |

ISBN (Electronic) | 9781493916009 |

DOIs | |

State | Published - Jan 1 2014 |

Event | School on Combinatorics, Automata and Number Theory, CANT 2012 - Marseille, France Duration: May 21 2012 → May 25 2012 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
---|---|

Volume | 101 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | School on Combinatorics, Automata and Number Theory, CANT 2012 |
---|---|

Country | France |

City | Marseille |

Period | 5/21/12 → 5/25/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Combinatorial and Additive Number Theory - CANT 2011 and 2012*(pp. 43-53). (Springer Proceedings in Mathematics and Statistics; Vol. 101). Springer New York LLC. https://doi.org/10.1007/978-1-4939-1601-6_4

}

*Combinatorial and Additive Number Theory - CANT 2011 and 2012.*Springer Proceedings in Mathematics and Statistics, vol. 101, Springer New York LLC, pp. 43-53, School on Combinatorics, Automata and Number Theory, CANT 2012, Marseille, France, 5/21/12. https://doi.org/10.1007/978-1-4939-1601-6_4

**Lower and upper classes of natural numbers.** / Haddad, L.; Helou, Charles.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Lower and upper classes of natural numbers

AU - Haddad, L.

AU - Helou, Charles

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We consider a partition of the subsets of the natural numbers ℕ into two classes, the lower class and the upper class, according to whether the representation function of such a subset A, counting the number of pairs of elements of A whose sum is equal to a given integer, is bounded or unbounded. We give sufficient criteria for two subsets of ℕ to be in the same class and for a subset to be in the lower class or in the upper class.

AB - We consider a partition of the subsets of the natural numbers ℕ into two classes, the lower class and the upper class, according to whether the representation function of such a subset A, counting the number of pairs of elements of A whose sum is equal to a given integer, is bounded or unbounded. We give sufficient criteria for two subsets of ℕ to be in the same class and for a subset to be in the lower class or in the upper class.

UR - http://www.scopus.com/inward/record.url?scp=84927630040&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927630040&partnerID=8YFLogxK

U2 - 10.1007/978-1-4939-1601-6_4

DO - 10.1007/978-1-4939-1601-6_4

M3 - Conference contribution

AN - SCOPUS:84927630040

T3 - Springer Proceedings in Mathematics and Statistics

SP - 43

EP - 53

BT - Combinatorial and Additive Number Theory - CANT 2011 and 2012

A2 - Nathanson, Melvyn B.

PB - Springer New York LLC

ER -