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More large sets of resolvable MTS and DTS with even orders

More large sets of resolvable MTS and DTS with even orders In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q + 2, or LRMTS(2q + 2), where q = 6t + 5 is a prime power. Using a computer, we find examples of such structure for t ∈ T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS(v) and LRDTS(v), where v = $$ 12(t + 1)\prod\limits_{m_i \geqslant 0} {(2 \cdot 7^{m_i } + 1)} \prod\limits_{n_i \geqslant 0} {(2 \cdot 13^{n_i } + 1)} $$ and t ∈ T, which provides more infinite family for LRMTS and LRDTS of even orders. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

More large sets of resolvable MTS and DTS with even orders

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-005-5206-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q + 2, or LRMTS(2q + 2), where q = 6t + 5 is a prime power. Using a computer, we find examples of such structure for t ∈ T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS(v) and LRDTS(v), where v = $$ 12(t + 1)\prod\limits_{m_i \geqslant 0} {(2 \cdot 7^{m_i } + 1)} \prod\limits_{n_i \geqslant 0} {(2 \cdot 13^{n_i } + 1)} $$ and t ∈ T, which provides more infinite family for LRMTS and LRDTS of even orders.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Aug 6, 2008

References