Wan Xi Chou

Construction and Enumenation of Multiple-Element Systems of Order v

This paper gives a constructed the multiple-element systems of order v the definitions about both derived design andcomplemented design. It proposes an algorithm of constructing bothderived design andcomplement design. It presents the entire procedure of constructing design and design, and discusses the enumeration problem of both derived design and complemented design.

Construction and Enumeration of Steiner Triple Systems with Order V

This paper describes the basic concept of constructing the large sets of Steiner triple systems of order v. It proposes a method of constructing the large sets of Steiner triple systems by using permutation of original matrix, and it presents entire procedure of constructing the large sets of Steiner triple systems of order 7. It verified the number of disjoint Steiner triple systems.

Methods of Constructing and Enumerating the Steiner Triple System with Order 31

This paper describes the basic concept of constructing Steiner triple system of order and gives the definition edge matrix of a complete graph. It proposes a method of constructing Steiner triple system of order. The entire procedure of constructing Steiner triple system of order .It discusses the enumeration problem of Steiner triple system.

A Method of Constructing Steiner Triple System of Order 2t+1

The basic concept of constructing the Steiner triple systems of order is described. The detinition of edges matrix of the complete graph is given. A method of constructing Steiner triple system of order is proposed. The errtire procedure of constructing Steiner triple systems of orderand is presented respectively, The enumeration problem of Steiner triple systems of order is discussed [1-1.

The Construction of Disjoint Multiple-Element Systems with v Order

Clarify the properties of derived design and complement design. The properties of Abstract: The definitions of derived design and complementary design are given. The method of constructing disjoint (13,4,1) design is proposed. The entire procedure of constructing (14,3,1) design ,(26,13,8,4,2) design and (13,9,6) design is also presented completely. 15 disjoint (13,4,1) design , 15 disjoint (13,9,6) design and 7 disjoint (26,13,8,4,2) design are obtained. The number of disjoint (13, 4, 1) design is proved.

Methods of Constructing and Enumerating the Spanning Tree of a Connected Graph

A definition concerning the spanning sub graph and spanning sub graph circle is given. Use the enumerating methods of spanning sub circle; seek out the spanning sub graph of spanning trees. The theorems of constructing and enumerating the spanning trees are proved. The methods of enumerating and constructing connected graph spanning tree are proposed. The application examples of construction theorem and enumerating theorem are given. the spanning sub graphs number of five plane graph and the construction of Constituent sub-graph are introduced, thus verifying constructing and enumerating theorem are useful and effective. This method Is a Simple and easy method to construct the spanning tree of connected graph.

A Construction Method of Large V Order Steiner Four Elements Large Set

This paper proposed the basic idea of constructing method of large v order Steiner four elements large set under the blow of steiner three elements. At the same, this paper analyzed the conditions for the existence of v order Steiner four elements. This paper also proposed the construction method of v order Steiner four elements large set based on the initial block matrix permutation. This paper also introduced the entire construction process of 9 order Steiner four elements systems large set. This paper proved the number of 9 order Steiner four elements s(1)(9)of 9 order Steiner four elements large set is d(9)=v-8=1 .

Two Isomorphic 9 Order Steiner Triple Systems Large Sets

This paper Clarifies the basic ideas of constructing the v order Steiner triple systems. This paper proposed the construction method of pairwise disjoint sets s(i)(v) for Steiner triple systems based on the initial block permutation matrix. And a method of initial block permutation matrix is given. This paper also introduced the entire construction process of two isomorphic 9 order Steiner triple systems large set. At last, this paper proved the number of pairwise disjoint forsi(9)is d(9)=7 .

Design and Construct for Non-Isomorphism Block

This paper clarifies the basic idea of design and construct for non-isomorphism block. The method of using standard edge matrix to structure block design is proposed, the whole process to design and construct (14, 8, 7, 4, 3) and (18, 9, 8, 4, 3) is introduced. It uses the side of each column of the standard edge matrix exactly, and also constitutes a complete graph by arranging the edge of complete graph to the initial matrix and re-arranging it to the standard edge matrix. According to the set of edge in standard edge matrix, 14 blocks of designing (14,8,7,4,3) and 18 blocks of designing (18,9,8,4,3) are obtained. Finally, it proved the number of design non-isomorphism (14, 8, 7, 4, 3) is 5, and (14, 8, 7, 4, 3) is 1.

Constructing of Multiple-Element Systems with V Order

This paper gives the definitions of exported design and residual design is given. The relation of order between derived design and residual design has been clarified. The blocks capacity in derived design are and the blocks capacity in residual design are . The number of non-isomorphism derived design is equal to the residual design. If the incidience matrix of derived design is , then the incidience matrix of residual design is . The blocks in derived design and the blocks in residual design exist the complementary relationship. The construction methods of derived design and residual design have been proposed. The entire procedure of constructing (15,7,3) derived design and (15,8,2) residual design is also presented completely.