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On the number of mutually disjoint cyclic designs | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 3، شماره 1، خرداد 2014، صفحه 7-13 اصل مقاله (331.4 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.3820 | ||
| نویسندگان | ||
| Mojgan Emami* ؛ Ozra Naserian | ||
| Department of Mathematics, University of Zanjan | ||
| چکیده | ||
| We denote by $LS[N](t,k,v)$ a large set of $t$-$(v,k,\lambda)$ designs of size $N$, which is a partition of all $k$-subsets of a $v$-set into $N$ disjoint $t$-$(v,k,\lambda)$ designs and $N={v-t \choose k-t}/\lambda$. We use the notation $N(t,v,k,\lambda)$ as the maximum possible number of mutually disjoint cyclic $t$-$(v,k,\lambda)$designs. In this paper we give some new bounds for $N(2,29,4,3)$ and $N(2,31,4,2)$. Consequently we present new large sets $LS[9](2,4,29), LS[13](2,4,29)$ and $LS[7](2,4,31)$, where their existences were already known. | ||
| کلیدواژهها | ||
| Large Set؛ $t$-Design؛ Kramer-Mesner Matrix | ||
| مراجع | ||
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L. Bluskov and S. S. Magliveras (2001) On the number of mutually disjoint cyclic designs and large sets of designs J. Statist. Plann. Inference 95, 133-142
M. Emami and O. Naserian (2010) Some new large sets of $t$-designs Discrete Math. 310, 1629-1632
G. B. Khosrovshahi and R. Laue (2007) $t$-Designs, t\leq 3 , in:
Handbook of combinatorial designs 2nd ed. (C. J. Colbourn and J.
H. Dinitz, eds.) CRC press, Boca Raton , 98-110
G. B. Khosrovshahi, R. Laue and B. Tayfeh-Rezaie (2005) On large sets
of t-design of size four Bayreuth. Math. Schr. (74), 136-144
E. S. Kramer and D. M. Mesner (1976) t-designs on hypergraphs Discrete Math. 15, 263-296
R. Laue, S. S. Magliveras and A. Wassermann (2001) New large sets of
t-designs J. Combin. Des. 9, 40-59
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