| The spectrum for large sets of pure directed triple systems |
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| 引用本文： | ZHOU Junling,CHANG Yanxun & Jl Lijun Institute of Mathematics,Beijing Jiaotong University,Beijing 100044,China, Department of Mathematics,Suzhou University,Suzhou 215006,China. The spectrum for large sets of pure directed triple systems[J]. 中国科学A辑(英文版), 2006, 49(8): 1103-1127. DOI: 10.1007/s11425-006-2007-3 |
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| 作者姓名： | ZHOU Junling CHANG Yanxun & Jl Lijun Institute of Mathematics Beijing Jiaotong University Beijing 100044 China Department of Mathematics Suzhou University Suzhou 215006 China |
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| 作者单位： | ZHOU Junling，CHANG Yanxun & Jl Lijun Institute of Mathematics，Beijing Jiaotong University，Beijing 100044，China; Department of Mathematics，Suzhou University，Suzhou 215006，China |
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| 基金项目： | 国家自然科学基金;国家自然科学基金;江苏省自然科学基金 |
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| 摘 要： | An LPDTS(ν) is a collection of 3(ν-2) disjoint pure directed triple systems on the same set ofνelements. It is showed in Tian's doctoral thesis that there exists an LPDTS(ν) forν=0,4 (mod 6),ν≥4. In this paper, we establish the existence of an LPDTS(ν) forν= 1,3 (mod 6),ν> 3. Thus the spectrum for LPDTS(ν) is completely determined to be the set {ν:ν= 0, 1 (mod 3),ν≥4}.
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| 收稿时间： | 2005-09-27 |
| 修稿时间： | 2006-03-28 |
The spectrum for large sets of pure directed triple systems |
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| ZHOU Junling,CHANG Yanxun,JI Lijun. The spectrum for large sets of pure directed triple systems[J]. Science in China(Mathematics), 2006, 49(8): 1103-1127. DOI: 10.1007/s11425-006-2007-3 |
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| Authors: | ZHOU Junling CHANG Yanxun JI Lijun |
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| Affiliation: | 1. Institute of Mathematics, Beijing Jiaotong University, Beijing 100044, China
2. Department of Mathematics, Suzhou University, Suzhou 215006, China |
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| Abstract: | An LPDTS(ν) is a collection of 3(ν − 2) disjoint pure directed triple systems on the same set of ν elements. It is showed in Tian’s doctoral thesis that there exists an LPDTS(gn) for gn ≡ 0,4 (mod 6), ν ⩾ 4. In this paper, we establish the existence of an LPDTS(ν) for ν ≡ 1,3 (mod 6), ν > 3. Thus the spectrum for LPDTS(ν) is completely determined to be the set {ν:ν ≡ 0, 1 (mod 3), ν ⩾ 4}. |
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| Keywords: | large set oriented triple system pure directed candelabra system |
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