Two Isomorphic 9 Order Steiner Triple Systems Large Sets

Xu, Zhao Di; Li, Xiao Yi; Chou, Wan Xi

doi:10.4028/www.scientific.net/AMM.427-429.1237

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Two Isomorphic 9 Order Steiner Triple Systems Large Sets

Abstract:

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 .

Info:

Periodical:

Applied Mechanics and Materials (Volumes 427-429)

Main Theme:

Mechanical Engineering, Industrial Electronics and Information Technology Applications in Industry

Edited by:

B. L. Liu, Minghai Yuan, Guorong Chen and Jun Peng

Pages:

1237-1240

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.427-429.1237

Citation:

Z. D. Xu et al., "Two Isomorphic 9 Order Steiner Triple Systems Large Sets", Applied Mechanics and Materials, Vols. 427-429, pp. 1237-1240, 2013

Online since:

September 2013

Authors:

Zhao Di Xu *, Xiao Yi Li, Wan Xi Chou

Keywords:

Large Set, Matrix, Permutation, Steiner Triple System, Structure

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References

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Paper TitlePages

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

Authors: Xiao Yi Li, Zhao Di Xu, Wan Xi Chou

Abstract: 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 .

379

Construction and Enumeration of Steiner Triple Systems with Order V

Authors: Zhao Di Xu, Xiao Yi Li, Wan Xi Chou

Abstract: 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.

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