Abstract
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 language | English (US) |
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Article number | 113396 |
Journal | Discrete Mathematics |
Volume | 346 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2023 |
Keywords
- Bose triple system
- Kirkman triple system
- Latin square
- Resolvability
- Steiner triple system
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics