# The spectrum for overlarge sets of hybrid triple systems

The spectrum for overlarge sets of hybrid triple systems A hybrid triple system of order v and index λ, denoted by HTS(v, λ), is a pair (X, B) where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to λ triples of B. An overlarge set of disjoint HTS(v, λ), denoted by OLHTS(v, λ), is a collection {(Y\ {y}, A i )} i , such that Y is a (v + 1)-set, each (Y \{y}, A i ) is an HTS(v, λ) and all A i s form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS(v, λ) and give the following conclusion: there exists an OLHTS(v, λ) if and only if λ = 1, 2, 4, v ≡ 0,1 (mod 3) and v ≥ 4. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# The spectrum for overlarge sets of hybrid triple systems

, Volume 30 (3) – Nov 6, 2014
12 pages

/lp/springer-journals/the-spectrum-for-overlarge-sets-of-hybrid-triple-systems-860nx0qIFV
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-014-0417-5
Publisher site
See Article on Publisher Site

### Abstract

A hybrid triple system of order v and index λ, denoted by HTS(v, λ), is a pair (X, B) where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to λ triples of B. An overlarge set of disjoint HTS(v, λ), denoted by OLHTS(v, λ), is a collection {(Y\ {y}, A i )} i , such that Y is a (v + 1)-set, each (Y \{y}, A i ) is an HTS(v, λ) and all A i s form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS(v, λ) and give the following conclusion: there exists an OLHTS(v, λ) if and only if λ = 1, 2, 4, v ≡ 0,1 (mod 3) and v ≥ 4.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 6, 2014

### References

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