The spectrum of resolvable Bose triple systems

Research output: Contribution to journalArticlepeer-review


A classical construction of Bose produces a Steiner triple system of order 3n from a symmetric, idempotent latin square of order n, which exists whenever n is odd. In an application to access-balancing in storage systems, certain Bose triple systems play a central role. A natural question arises: For which orders v does there exist a resolvable Bose triple system? Elementary counting establishes the necessary condition that v≡9(mod18). For specific Bose triple systems that optimize an access metric, we show that v≡9(mod18) is also sufficient.

Original languageEnglish (US)
Article number113396
JournalDiscrete Mathematics
Issue number7
StatePublished - Jul 2023


  • Bose triple system
  • Kirkman triple system
  • Latin square
  • Resolvability
  • Steiner triple system

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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