### 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) |
---|---|

Pages (from-to) | 107-118 |

Number of pages | 12 |

Journal | North-Holland Mathematics Studies |

Volume | 149 |

Issue number | C |

DOIs | |

State | Published - 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

**Partitions into Indecomposable Triple Systems.** / Colbourn, Charles; Harms, Janelle J.

Research output: Contribution to journal › Article

*North-Holland Mathematics Studies*, vol. 149, no. C, pp. 107-118. https://doi.org/10.1016/S0304-0208(08)72879-2

}

TY - JOUR

T1 - Partitions into Indecomposable Triple Systems

AU - Colbourn, Charles

AU - Harms, Janelle J.

PY - 1987

Y1 - 1987

N2 - 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 λ1 + ... +λs = 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.

AB - 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 λ1 + ... +λs = 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.

UR - http://www.scopus.com/inward/record.url?scp=33750694810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750694810&partnerID=8YFLogxK

U2 - 10.1016/S0304-0208(08)72879-2

DO - 10.1016/S0304-0208(08)72879-2

M3 - Article

AN - SCOPUS:33750694810

VL - 149

SP - 107

EP - 118

JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

SN - 0304-0208

IS - C

ER -