### Abstract

The indecomposable partition problem is to partition the set of all triples on v elements into s indecomposable triple systems, where the i th triple system has index λ_{i} and λ_{1} + … +λ_{s} = v–2. A complete solution for v ≤ 10 is given here. Extending a construction of Rosa for large sets, we then give a v → 2v + 1 construction for indecomposable partitions. This recursive construction employs solutions to a related partition problem, called indecomposable near-partition. A partial solution to the indecomposable near-partition problem for v = 10 then establishes that for every order v = 5.2^{i}–1, all indecomposable partitions having λ_{i} = 1,2 for each i can be realized.

Original language | English (US) |
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Pages (from-to) | 107-118 |

Number of pages | 12 |

Journal | North-Holland Mathematics Studies |

Volume | 149 |

Issue number | C |

DOIs | |

State | Published - Jan 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*North-Holland Mathematics Studies*,

*149*(C), 107-118. https://doi.org/10.1016/S0304-0208(08)72879-2