TY - JOUR
T1 - The spectrum of resolvable Bose triple systems
AU - Lusi, Dylan
AU - Colbourn, Charles J.
N1 - Funding Information:
Research supported by NSF grant CCF 1814298 (CJC). Thanks to Ryan Gabrys and Olgica Milenkovic for helpful discussions. Thanks also to two constructive and thorough reviewers.
Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/7
Y1 - 2023/7
N2 - 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.
AB - 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.
KW - Bose triple system
KW - Kirkman triple system
KW - Latin square
KW - Resolvability
KW - Steiner triple system
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U2 - 10.1016/j.disc.2023.113396
DO - 10.1016/j.disc.2023.113396
M3 - Article
AN - SCOPUS:85149483411
SN - 0012-365X
VL - 346
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 7
M1 - 113396
ER -