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| 1 | Construction of optimal supersaturated designs by the packing method显示文摘A supersaturated design is essentially a factorial design with the equal occurrence of levels property and no fully aliased factors in which the number of main efits potential in factor screening experiments. A packing design is an important object in combinatorial design theory. In this paper, a strong link between the two apparently unrelated kinds of designs is shown. Several criteria for comparing supersaturated designs are proposed, their properties and connections with other existing criteria are discussed.A combinatorial approach, called the packing method, for constructing optimal supersaturated designs is presented, and properties of the resulting designs are also investigated.Comparisons between the new designs and other existing designs are given, which show that our construction method and the newly constructed designs have good properties. | FANG Kaitai GE Gennian LIU Minqian | 2004 | Science China Mathematics2004，47，1： | 4 |
| 2 | Constructions for optimal( v,4, 1 ) optical orthogonal codes显示文摘 | Gennian ge Jianxing Yin | 2001 | IEEE trans on Information Theory2001，47，11： | 1 |
| 3 | Constructions for optimal(v,4,1)optical orthogonal codes显示文摘 | GE Gennian YIN Jianxing | | 0，，11： | 1 |
| 4 | Further combinatorial constructions for optimal frequency-hopping sequences显示文摘 | Gennian Ge Ryoh Fuji-Hara Ying Miao | 2006 | Journal of Combinatorial Theory A2006，113，： | 1 |
| 5 | Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves显示文摘 | Li Shuxing Gao Fei Ge Gennian | 2012 | IEEE Transactions on Information Theory2012，58，8： | 1 |
| 6 | Uniform supersaturated design and its construction显示文摘 | Kaitai Fang Gennian Ge Minqian Liu | 2002 | Science in China Series A: Mathematics2002，，8： | 1 |
| 7 | Deterministic construction of sparse sensing matrices via finite geometry显示文摘 | LI Shuxing GE Gennian | 2014 | IEEE Transactions on Signal Processing2014，62，11： | 1 |
| 8 | Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves显示文摘 | Li Shuxing Gao Fei Ge Gennian | 2012 | IEEE Transactions on Information Theory2012，58，8： | 1 |
| 9 | Combinatorial Characteriza- tions of One-Coincidence Frequence-Hopping Sequences 显示文摘 | Zhenfu Cao Gennian Ge Ying Miao | 2006 | Des Codes Crypt2006，41，： | 1 |
| 10 | Deterministic construction of sparse sensingmatricesviafinitegeometry显示文摘 | LI SHUXING GE GENNIAN | 2014 | IEEE Trans on Signal Processing2014，62，： | 1 |
| 11 | Some extremal results on hypergraph Turán problems显示文摘For two r-graphs T and H,let ex_(r)(n,T,H)be the maximum number of copies of T in an n-vertex H r-graph.The determination of the Turán number ex_(r)(n,T,H)has become the fundamental core problem in extremal graph theory ever since the pioneering work of Turán’s theorem was published in 1941.Although we have some rich results for the simple graph case,only sporadic results have been known for the hypergraph Turán problems.In this paper,we mainly focus on the function ex_(r)(n,T,H)when H is one of two different hypergraph extensions of the complete bipartite graph K_(s,t).The first extension is the complete bipartite r-graph K^((r))_(s,t),which was introduced by Mubayi and Verstraëte(2004).Using the powerful random algebraic method,we show that if s is sufficiently larger than t,then ex_(r)(n,T,K^((r))_(s,t))=Ω(n^(v−e/t)),where T is an r-graph with v vertices and e edges.In particular,when T is an edge or some specified complete bipartite r-graph,we can determine their asymptotics.The second important extension is the complete r-partite r-graph K^((r))_(s1,s2,…,sr,)which has been widely studied.When r=3,we provide an explicit construction giving ex_(3)(n,K^((3))_(2,2,7))≥1/27n19/7+o(n19/7).Our construction is based on the norm graph,and improves the lower boundΩ(n73/27)obtained by the probabilistic method. | Zixiang Xu Tao Zhang Gennian Ge | 2022 | Science China Mathematics2022，65，8： | 0 |
| 12 | Some intriguing upper bounds for separating hash families显示文摘An N ×n matrix on q symbols is called {w_1,...,w_t}-separating if for arbitrary t pairwise disjoint column sets C_1,..., C_t with |C_i|=w_i for 1 ≤i≤t, there exists a row f such that f(C_1),...,f(C_t) are also pairwise disjoint, where f(C_i) denotes the collection of componentn of C_i restricted to row f. Given integers N, q and w_1,...,w_t, denote by C(N,q,{w_1,...,w_t}) the maximal a such that a corresponding matrix does exist.The determination of C(N,q,{w_1,...,w_t}) has received remarkable attention during the recent years. The main purpose of this paper is to introduce two novel methodologies to attack the upper bound of C(N, q, {w_1,...,w_t}).The first one is a combination of the famous graph removal lemma in extremal graph theory and a Johnson-type recursive inequality in coding theory, and the second onc is the probabilistic method. As a consequence, we obtain several intriguing upper bounds for some parameters of C(N,q,{w_1,...,w_t}), which significantly improve the previously known results. | Gennian Ge Chong Shangguan Xin Wang | 2019 | Science China Mathematics2019，62，2： | 0 |
| 13 | Inverse problems of the Erdos-Ko-Rado type theorems for families of vector spaces and permutations显示文摘Ever since the famous Erd os-Ko-Rado theorem initiated the study of intersecting families of subsets,extremal problems regarding intersecting properties of families of various combinatorial objects have been extensively investigated.Among them,studies about families of subsets,vector spaces and permutations are of particular concerns.Recently,we proposed a new quantitative intersection problem for families of subsets:For F([n]k),define its total intersection number as I(F)=ΣF1;F2∈F|F1∩F2|.Then,what is the structure of F when it has the maximal total intersection number among all the families in([n]k)with the same family size?In a recent paper,Kong and Ge(2020)studied this problem and characterized extremal structures of families maximizing the total intersection number of given sizes.In this paper,we consider the analogues of this problem for families of vector spaces and permutations.For certain ranges of family sizes,we provide structural characterizations for both families of subspaces and families of permutations having maximal total intersection numbers.To some extent,these results determine the unique structure of the optimal family for some certain values of jFj and characterize the relationship between having the maximal total intersection number and being intersecting.Besides,we also show several upper bounds on the total intersection numbers for both families of subspaces and families of permutations of given sizes. | Xiangliang Kong Yuanxiao Xi Bingchen Qian Gennian Ge | 2022 | Science China Mathematics2022，65，5： | 0 |
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