TY - JOUR
T1 - Trails of triples in partial triple systems
AU - Colbourn, Charles
AU - Horsley, Daniel
AU - Wang, Chengmin
N1 - Funding Information:
Acknowledgments Chengmin Wang is supported by NSFC under Grant Nos. 10801064, 11001109, and 10926103, and by the Program for Innovative Research Team of Jiangnan University.
PY - 2012/12
Y1 - 2012/12
N2 - 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).
AB - 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).
KW - Kirkman signal set
KW - Kirkman triple system Hanani triple system
KW - Resolvable triple system
KW - Steiner triple system
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U2 - 10.1007/s10623-011-9521-1
DO - 10.1007/s10623-011-9521-1
M3 - Article
AN - SCOPUS:84868361050
SN - 0925-1022
VL - 65
SP - 199
EP - 212
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 3
ER -