The Existence of LHMTS(m v ) and LHDTS(m v )

The Existence of LHMTS(m v ) and LHDTS(m v ) Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 18, 2018 https://doi.org/10.1007/s10114-018-7306-4 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 v v The Existence of LHMTS(m ) and LHDTS(m ) Xiang Qian LI Institute of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R.China E-mail : 625585228@qq.com 1) Ru Hong HU Zi Hong TIAN College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024,P.R. China E-mail : 1548334942@qq.com tianzh68@163.com )for v ≡ 2(mod 6) and m ≡ 3 Abstract In this article, we establish the existence of an LHMTS(m v 2 (mod 6). Thus there exists an LHMTS(m ) if and only if v(v − 1)m ≡ 0 (mod 3) except possibly for v =6, m ≡ 1,5(mod 6) and m = 1. In the similar way, the existence of LHDTS(m ) is completely v 2 determined, i.e., there exists an LHDTS(m ) if and only if v(v − 1)m ≡ 0(mod 3). Keywords Holey Mendelsohn triple system, holey directed triple system, large set MR(2010) Subject Classification 05B05, 05B07 1 Introduction A group-divisible design GDD(t, K, u; n {g },n {g },... ,n {g }) is a triple (X, G, B) such that: http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

The Existence of LHMTS(m v ) and LHDTS(m v )

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Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Copyright
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-018-7306-4
Publisher site
See Article on Publisher Site

Abstract

Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 18, 2018 https://doi.org/10.1007/s10114-018-7306-4 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 v v The Existence of LHMTS(m ) and LHDTS(m ) Xiang Qian LI Institute of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R.China E-mail : 625585228@qq.com 1) Ru Hong HU Zi Hong TIAN College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024,P.R. China E-mail : 1548334942@qq.com tianzh68@163.com )for v ≡ 2(mod 6) and m ≡ 3 Abstract In this article, we establish the existence of an LHMTS(m v 2 (mod 6). Thus there exists an LHMTS(m ) if and only if v(v − 1)m ≡ 0 (mod 3) except possibly for v =6, m ≡ 1,5(mod 6) and m = 1. In the similar way, the existence of LHDTS(m ) is completely v 2 determined, i.e., there exists an LHDTS(m ) if and only if v(v − 1)m ≡ 0(mod 3). Keywords Holey Mendelsohn triple system, holey directed triple system, large set MR(2010) Subject Classification 05B05, 05B07 1 Introduction A group-divisible design GDD(t, K, u; n {g },n {g },... ,n {g }) is a triple (X, G, B) such that:

Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 18, 2018

References

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