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The Fine Structures of Three Symmetric Latin Squares with Even Orders

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Acta Mathematica Sinica,English Series 2011年第6期27卷 1137-1148页

作者： Er Qiang FENG yan xun chang Institute of Mathematics Beijing Jiaotong University Beijing 100044 P. R. China

Denote by SFin（v） the set of all integer pairs （t, s） for which there exist three symmetric Latin squares of order v on the same set having fine structure （t, s）. We completely determine the set SFin（2n） for a... 详细信息

关键词： Symmetric Latin square symmetric Latin trade fine structure

Tripling Construction for Large Sets of Resolvable Directed Triple Systems

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Acta Mathematica Sinica,English Series 2006年第1期22卷 311-318页

作者： Jun Ling ZHOU yan xun chang Department of Mathematics Beijing Jiaotong University Beijing 100044 P. R. China

In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.

关键词： Doubly transitive resolvable idempotent quasigroup Resolvable directed triple system,Large set Tripling construction

The Fine Triangle Intersections for Maximum Kite Packings

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Acta Mathematica Sinica,English Series 2013年第5期29卷 867-882页

作者： Gui Zhi ZHANG yan xun chang Tao FENG Institute of Mathematics Beijing Jiaotong University School of Mathematical Sciences Hulunbuir College

In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin（v） = {（s, t）： E← a pair of maximum kite packings of order v intersecting in s blocks and s ＋ t triangles}. Let Adm（v） = {（s,t）： s ＋ t≤by, s, t are non-negative integers}, where by = [v（v - 1）/8]. It is established that Fin（v） = Adm（v）／{（bv - 1,0）, （by - 1, 1）} for any integer v - 0, 1 （rood 8） and v ≥ 8; Fin（v） = Adm（v） for any integer v = 2, 3, 4, 5, 6, 7 （rood 8） and v≥ 4.

关键词： Kite packing triangle intersection fine triangle intersection

Simple Minimum(K_4-e)-coverings of Complete Multipartite Graphs

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Acta Mathematica Sinica,English Series 2019年第5期35卷 632-648页

作者： Yu Feng GAO yan xun chang Tao FENG Institute of Mathematics Beijing Jiaotong University College of Mathematics Tonghua Normal University

A decomposition of K_(n(g))∪Γ, the complete n-partite equipartite graph over gn vertices union a graph Γ(called the excess) that is a subgraph of K_(n(g)), into edge disjoint copies of a graph G is called a simple minimum group divisible covering of type g^n with G if Γ contains as few edges as possible. We examine all possible excesses for simple minimum group divisible(K_4-e)-*** and sufficient conditions are established for their existence.

关键词： Group divisible covering (K4-e)-covering excess graph

The Spectrum of (gv, g, 3, λ)-dDF in Z_(gv)

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Acta Mathematica Sinica,English Series 2010年第2期26卷 377-392页

作者： Xiao Miao WANG yan xun chang Institute of Mathematics Beijing Jiaotong University Beijing 100044 P. R. China

In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a （gv, g, 3, λ）-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.

关键词： directed difference family incomplete difference matrix perfect directed difference family

Decompositions of the 3-uniform hypergraphs K_v^(3) into hypergraphs of a certain type

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Science China Mathematics 2007年第7期50卷 1035-1044页

作者： Tao FENG yan-xun chang Institute of Mathematics,Beijing Jiaotong University,Beijing 100044,China 1. Institute of Mathematics Beijing Jiaotong University Beijing 100044 China

In this paper,we investigate a generalization of graph decomposition,called hypergraph *** show that a decomposition of a 3-uniform hypergraph K_v^(3)into a special kind of hypergraph K_4^(3)-e exists if and only if v... 详细信息

关键词： hypergraph decomposition t-GDD group divisible(Γ,t)-design candelabra(Γ,t)-system

The Spectrum of (gv, g, 3, λ)-dDF in Zgv

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Acta Mathematica Sinica,English Series 2010年第2期26卷 377-392页

作者： Xiao Miao WANG yan xun chang Institute of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China Institute of Mathematics Beijing Jiaotong University Beijing P. R. China

In this paper, several recursive constructions for directed difference family and perfectdirected difference family are presented by means of difference matrix and incomplete difference *** the necessary and sufficient conditions for the existence of a (gv, g, 3, λ)-directed differencefamily in Zare established. As a consequence, the necessary and sufficient conditions for the existenceof a cyclic directed group divisible design with block size three and type g~v are obtained.

关键词： directed difference family incomplete difference matrix perfect directed difference family

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LD设计的存在谱

数学学报（中文版） 2023年第6期66卷 1019-1030页

作者：常彦勋谭霜飞周君灵北京交通大学数学与统计学院北京100044

在解决斯坦纳三元系大集存在性问题时,陆家羲引入LD设计和LD^(*)设计的概念,建立这两类设计的若干递推构造和直接构造,在构作斯坦纳三元系大集过程中发挥重要作用.为了构造陆家羲遗留的六个小阶数的斯坦纳三元系大集,Teirlinck依然借助L... 详细信息

在解决斯坦纳三元系大集存在性问题时,陆家羲引入LD设计和LD^(*)设计的概念,建立这两类设计的若干递推构造和直接构造,在构作斯坦纳三元系大集过程中发挥重要作用.为了构造陆家羲遗留的六个小阶数的斯坦纳三元系大集,Teirlinck依然借助LD设计,使用PBD进行递推构造,最终确定斯坦纳三元系大集的存在谱.本文将彻底解决LD设计存在的充分必要条件,对LD^(*)设计的存在性仅余四个可能例外值.

关键词： LD设计 LD^(*)设计正交表幂等拟群

Electroacupuncture modulate cortical activities evoked by noxious stimulation in human

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Electroacupuncture modulate cortical activities evoked by no...