Construction and Enumeration of Steiner Triple Systems with Order V

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.

• Periodical: Applied Mechanics and Materials (Volumes 496-500)
• Pages: 2355-2358
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.496-500.2355
• Online since: January 2014
• Authors: Zhao Di Xu, Xiao Yi Li, Wan Xi Chou
• Keywords: Construction, Disjoint, Large Sets, Steiner Triple System

References

[1] Richard A. bruald. Introductory Combinatorics[M]. Amsterdam: North-Holland Publishing Company, (1997).

[2] J.H. vanLint, R.M. Wilson. A Course in Combinatorics[M]. Beijing: China Machine Press, (2004).

[3] CHOU Wan-xi. A Method of Constructing Kirkman Triple System of Order[J]. Mathematics In Practice and Theory, 2004, 34(9): 144-150.

[4] TIAN Jin-ting, ZHANG Ying-shan, ZHANG Xiao-qin. The Comparison and Application of Balanced Block Orthogonal Arrays and Orthogonal Arrays[J]. Mathematics in Practice and Theory, 2009, 39(22): 59-67.

[5] H. Cao, Y. Tang. On Kirkman packing designs KPD({3, 4}, v)[J]. Discrete Mathematics, 2004, 279(1-3): 121-133.

DOI: 10.1016/s0012-365x(03)00263-2

[6] K. Daniel, M. Edita, P. Attila, J.S. Sereni. Characterization of affine Steiner triple systems and Hall triple systems[J]. Electronic Notes in Discrete Mathematics, 2007, 29: 17-21.

DOI: 10.1016/j.endm.2007.07.004

[7] Zhang S, Zhu L. An improved product construction for large sets of Kirkman triple systems[J]. Discrete mathematics, 2003, 260(1): 307-313.

DOI: 10.1016/s0012-365x(02)00766-5

[8] Hurd S P, Sarvate D G. An application of partition of indices to enclosings of triple systems[J]. Discrete Mathematics, 2003, 261(1): 337-346.

DOI: 10.1016/s0012-365x(02)00478-8

[9] Luo Chun, Pan Changyuan. Method of Exhaustion to Search Orthogonal Balanced Block Designs[J]. Applied Probability and Statistics, 2011, 27(1): 1-13.

[10] Jia-Xi L. On large sets of disjoint Steiner triple systems, VI[J]. Journal of Combinatorial Theory, Series A, 1984, 37(2): 189-192.

DOI: 10.1016/0097-3165(84)90068-2

[11] Teirlinck L. A completion of Lu's determination of the spectrum of large sets of disjoint Steiner triple systems[J]. J. Combin. Theory (A), 1991, 57: 302-305.

DOI: 10.1016/0097-3165(91)90053-j

[12] Ji L. A new existence proof for large sets of disjoint Steiner triple systems[J]. J. Combin. Theory(A), 2005, 112: 308-327.

DOI: 10.1016/j.jcta.2005.06.005

[13] A. Forbes, M. Grannell, T. Griggs, On 6-sparse Steiner triple systems, Journal of Combinatorial Theory, Series A, Vol. 114, No. 2, 235-252, (2007).

DOI: 10.1016/j.jcta.2006.04.003

[14] J. Zhou, Y. Chang, Existence of good large sets of Steiner triple systems, Discrete Mathematics, Vol. 309, No. 12, 3930-3935, (2009).

DOI: 10.1016/j.disc.2008.11.008

[15] M. Mariusz, R. Alexander, Embedding Steiner triple systems into Steiner systems S(2, 4, v), Discrete Mathematics, Vol. 274, No. 1-3, 199-212, (2004).

DOI: 10.1016/s0012-365x(03)00089-x

[16] L.J. Ji, J.G. Lei, Further results on large sets of Kirkman triple systems, Discrete Mathematics, Vol. 308, No. 20, 4643-4652, (2008).

DOI: 10.1016/j.disc.2007.08.081