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- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
- 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 Sinica – Springer Journals
Published: Nov 6, 2014