Two Isomorphic 9 Order Steiner Triple Systems Large Sets

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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 .

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Periodical:

Edited by:

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

Pages:

1237-1240

DOI:

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

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$38.00

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[1] Richard A. Bruald. Introductory Combinatiorics [M]. American: North-Holland Pubishing Company (1977).

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

[3] 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

[4] 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

[5] 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

[6] 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

[7] Král D, Máčajová E, Pór A, et al. Edge-colorings of cubic graphs with elements of point-transitive Steiner triple systems[J]. Electronic Notes in Discrete Mathematics, 2007, 29: 23-27.

DOI: 10.1016/j.endm.2007.07.005

[8] Zhou J, Chang Y. Existence of good large sets of Steiner triple systems[J]. Discrete Mathematics, 2009, 309(12): 3930-3935.

DOI: 10.1016/j.disc.2008.11.008

[9] Forbes A D. Uniquely 3-colourable Steiner triple systems[J]. Journal of Combinatorial Theory, Series A, 2003, 101(1): 49-68.

DOI: 10.1016/s0097-3165(02)00016-x

[10] Ji L, Lei J. Further results on large sets of Kirkman triple systems[J]. Discrete Mathematics, 2008, 308(20): 4643-4652.

DOI: 10.1016/j.disc.2007.08.081

[11] Lei J. On large sets of Kirkman triple systems and 3-wise balanced design[J]. Discrete mathematics, 2004, 279(1): 345-354.

DOI: 10.1016/s0012-365x(03)00279-6

[12] Forbes A D, Grannell M J, Griggs T S. On 6-sparse Steiner triple systems[J]. Journal of Combinatorial Theory, Series A, 2007, 114(2): 235-252.

DOI: 10.1016/j.jcta.2006.04.003

[13] Lindner C C, Quattrocchi G, Rodger C A. Embedding Steiner triple systems in hexagon triple systems[J]. Discrete Mathematics, 2009, 309(2): 487-490.

DOI: 10.1016/j.disc.2007.12.040

[14] Horak P. On the chromatic number of Steiner triple systems of order 25[J]. Discrete mathematics, 2005, 299(1): 120-128.

DOI: 10.1016/j.disc.2004.07.023

[15] Kaski P, ÖstergÅrd P R J, Topalova S, et al. Steiner triple systems of order 19 and 21 with subsystems of order 7[J]. Discrete Mathematics, 2008, 308(13): 2732-2741.

DOI: 10.1016/j.disc.2006.06.038

[16] Grannell M J, Griggs T S, Quinn K A S. Smallest defining sets of directed triple systems[J]. Discrete Mathematics, 2009, 309(14): 4810-4818.

DOI: 10.1016/j.disc.2008.06.021

[17] Král D, Máčajová E, Pór A, et al. 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

[18] Yin J, Wang C. Kirkman covering designs with even-sized holes[J]. Discrete Mathematics, 2009, 309(6): 1422-1434.

DOI: 10.1016/j.disc.2008.02.016

[19] Shen H, Wang Y. Embeddings of resolvable triple systems[J]. J of Combin Theory (A), 2000, 89 (1) : 21- 42.

[20] Shen H. Intersections of Kirkman triple systems[J]. Journal of statistical planning and inference, 2001, 94(2): 313-325.

DOI: 10.1016/s0378-3758(00)00262-7

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