Partitions into Indecomposable Triple Systems

Charles Colbourn, Janelle J. Harms

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 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.

Original languageEnglish (US)
Pages (from-to)107-118
Number of pages12
JournalNorth-Holland Mathematics Studies
Volume149
Issue numberC
DOIs
StatePublished - 1987
Externally publishedYes

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Triple System
Partition
Large Set
Partial

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: North-Holland Mathematics Studies, Vol. 149, No. C, 1987, p. 107-118.

Research output: Contribution to journalArticle

Colbourn, Charles ; Harms, Janelle J. / Partitions into Indecomposable Triple Systems. In: North-Holland Mathematics Studies. 1987 ; Vol. 149, No. C. pp. 107-118.
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