Trails of triples in partial triple systems

Charles Colbourn, Daniel Horsley, Chengmin Wang

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Given v, t, and m, does there exist a partial Steiner triple system of order v with t triples whose triples can be ordered so that any m consecutive triples are pairwise disjoint? Given v, t, and m 1,m 2,.. ,m s with t = Σ i=1 s m i, does there exist a partial Steiner triple system with t triples whose triples can be partitioned into partial parallel classes of sizes m 1,.. ,m s? An affirmative answer to the first question gives an affirmative answer to the second when m i ≥ m for each i ε {1, 2,.. ., s}. These questions arise in the analysis of erasure codes for disk arrays and that of codes for unipolar communication, respectively. A complete solution for the first problem is given when m is at most 1/3 (v - (9v) 2/3)+O(v 1/3).

Original languageEnglish (US)
Pages (from-to)199-212
Number of pages14
JournalDesigns, Codes, and Cryptography
Volume65
Issue number3
DOIs
StatePublished - Dec 1 2012

Keywords

  • Kirkman signal set
  • Kirkman triple system Hanani triple system
  • Resolvable triple system
  • Steiner triple system

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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