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On large sets of Kirkman triple systems and 3-wise balanced design

Jian-guo Lei
2004 Discrete Mathematics  
In this paper, the existence of large sets of Kirkman triple system is transformed to the existence of ÿnite OLKFs and LGKSs.  ...  As well, we present a construction of 3-wise balanced design.  ...  For example, a large set of disjoint Steiner triple systems, a large set of disjoint transitive triple systems, a large set of disjoint Mendelsohn triple systems, a large set of disjoint group-divisible  ... 
doi:10.1016/s0012-365x(03)00279-6 fatcat:qvr6zf3cpjckfoibeuqrhvu4g4

Author index to volume 279

2004 Discrete Mathematics  
Rodger, Hamilton decompositions of complete graphs with a 3-factor leave (1-3) 337-344 Lei, J., On large sets of Kirkman triple systems and 3-wise balanced design (1-3) 345-354 Li, P.C., see A.C.H.  ...  Tang, On Kirkman packing designs KPDðf3; 4g; vÞ (1-3) 121-133 Cao, Z., see K. Chen (1-3) 153-161 Chang, Y. and J.  ... 
doi:10.1016/s0012-365x(04)00071-8 fatcat:3mv4w7o4dbcrdit6x7bcxdgqsy

On large sets of Kirkman systems with holes

Jian-guo Lei
2002 Discrete Mathematics  
We study the large sets of generalized Kirkman systems. The purpose of introducing the structure is to construct the large sets of Kirkman triple systems (brie y LKTS).  ...  Our main result is that there exists an LKTS(v) for v ∈ {6 · 4 n 25 m + 3; m; n ¿ 0}.  ...  Zhu for helpful suggestions and the referees for their helpful comments.  ... 
doi:10.1016/s0012-365x(01)00295-3 fatcat:xmpjx3ivqrg3vlgnof2gzqgsaq

Page 416 of Mathematical Reviews Vol. 52, Issue 2 [page]

1976 Mathematical Reviews  
Chapter 2 introduces the class of combinatorial designs, includ- ing the finite planes and the pairwise balanced and group divisible designs.  ...  A collection U(N)={S(N)} of Steiner triple systems is said to be an OSS(n, t) if |U(N)|=t and, for S(N), SAN) € U(N), i#j, SN) is orthogonal to S(N).  ... 

Further results on large sets of Kirkman triple systems

Lijun Ji, Jianguo Lei
2008 Discrete Mathematics  
An LR design is introduced by the second author in his recent paper and it plays a very important role in the construction of LKTS (a large set of disjoint Kirkman triple system).  ...  In this paper, we generalize it and introduce a new design RPICS. Some constructions for these two designs are also presented. With the relationship between them and LKTS, we obtain some new LKTSs.  ...  Zhu for helpful suggestions on this topic and the referees for many helpful comments.  ... 
doi:10.1016/j.disc.2007.08.081 fatcat:zgwj7imc35cdhayalildu727yy

A tripling construction for overlarge sets of KTS

Landang Yuan, Qingde Kang
2009 Discrete Mathematics  
x ∈ X } forms a partition of all triples on X . In this paper, we give a tripling construction for overlarge sets of K T S.  ...  It is obtained that there exists an OLKTS(3 m (2u + 1)) for u = 2 2n−1 − 1 or u = q n , where prime power q ≡ 7 (mod 12) and m ≥ 0, n ≥ 1.  ...  forward the study of large sets of Kirkman triple systems.  ... 
doi:10.1016/j.disc.2008.01.001 fatcat:txbq2xqykvgfrddkumpdqnikz4

Recursive constructions and some properties of twofold designs with block size four

K. T. Phelps, A. Rosa
1988 Journal of the Australian Mathematical Society  
A direct construction for partially resolvable r-partitions is presented and then used to give a recursive construction for BIBDs (v,4,2).  ...  This result allows us to give simple proofs for the existence of B I B D ( u , 4 , 2 ) with various additioinal properties. 1980 Mathematics subject classification (Amer. Math. Soc): 05 B 05.  ...  (A /-partition is sometimes called a /-wise balanced design.) The elements of K are the block sizes.  ... 
doi:10.1017/s1446788700031372 fatcat:4g2r5rz6gzbkvg3lnkhpbbabmm

On large sets of disjoint Kirkman triple systems

Jian-guo Lei
2002 Discrete Mathematics  
In this paper, we introduce LR(u) designs and use these designs together with large sets of Kirkman triple systems (LKTS) and transitive KTS (TKTS) of order v to construct an LKTS(uv).  ...  Our main result is that there exists an LKTS(v) for v ∈ {3 n m(2 · 13 k + 1) t ; n ¿ 1; k ¿ 1; t = 0; 1; m ∈ {1; 5; 11; 17; 25; 35; 43}}.  ...  Zhu and the referees for helpful suggestions.  ... 
doi:10.1016/s0012-365x(01)00470-8 fatcat:g7rbpllc3bag7lgwedznvtu5i4

Kirkman Equiangular Tight Frames and Codes

John Jasper, Dustin G. Mixon, Matthew Fickus
2014 IEEE Transactions on Information Theory  
a combinatorial design and a regular simplex.  ...  We show that they are actually intimately connected: a large class of Steiner ETFs can be unitarily transformed into constant-amplitude frames, dubbed Kirkman ETFs.  ...  Note that when q = 2 this design is a (2, 3, 15)-Steiner triple system which, as noted above, generates an ETF which is not harmonic.  ... 
doi:10.1109/tit.2013.2285565 fatcat:vdrruap5mvegbb2m54xhh3cld4

Kirkman Equiangular Tight Frames and Codes [article]

John Jasper, Dustin G. Mixon, Matthew Fickus
2013 arXiv   pre-print
a combinatorial design and a regular simplex.  ...  We show that they are actually intimately connected: a large class of Steiner ETFs can be unitarily transformed into constant-amplitude frames, dubbed Kirkman ETFs.  ...  Note that when q = 2 this design is a (2, 3, 15)-Steiner triple system which, as noted above, generates an ETF which is not harmonic.  ... 
arXiv:1306.3111v1 fatcat:e3txx57hgfeftkr5ijf6hxzfea

A new existence proof for large sets of disjoint Steiner triple systems

L. Ji
2005 Journal of combinatorial theory. Series A  
For this purpose, we give a new proof which is mainly based on the 3-wise balanced designs and partitionable candelabra systems.  ...  A large set of disjoint STS(v) (briefly LSTS(v)) is a partition of all 3-subsets (triples) of X into v − 2 STS(v).  ...  Zhu for helpful suggestions and the referees for many helpful comments.  ... 
doi:10.1016/j.jcta.2005.06.005 fatcat:33fj5cn7xvc7nb46edvrnloieq

Asymptotically optimal erasure-resilient codes for large disk arrays

Yeow Meng Chee, Charles J. Colbourn, Alan C.H. Ling
2000 Discrete Applied Mathematics  
Reliability is a major concern in the design of large disk arrays.  ...  In this paper, we take a set systems view of the problem of constructing erasure-resilient codes. This leads to interesting extremal problems in ÿnite set theory.  ...  This work was begun while the authors were at the University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.  ... 
doi:10.1016/s0166-218x(99)00228-0 fatcat:3odz3oxd7zgfrfes2tyf6n4n5e

Classification of resolvable balanced incomplete block designs — the unitals on 28 points

Petteri Kaski, Patric Östergård
2009 Mathematica Slovaca  
With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs  ...  AbstractApproaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed.  ...  Consider the Kirkman triple system on 9 points, that is, the unique resolution of the unique 2-(9, 3, 1) BIBD.  ... 
doi:10.2478/s12175-009-0113-8 fatcat:soxakboa5jemlb46mri2eqmtmi

Existence of good large sets of Steiner triple systems

Junling Zhou, Yanxun Chang
2009 Discrete Mathematics  
The concept of good large set of Steiner triple systems (or GLS in short) was introduced by Lu in his paper "on large sets of disjoint Steiner triple systems", [J.  ...  Lu, On large sets of disjoint Steiner triple systems, I-III, J. Combin. Theory (A) 34 (1983) 140-182].  ...  Acknowledgement The research was supported by NSFC grants No. 10771013 and 10831002.  ... 
doi:10.1016/j.disc.2008.11.008 fatcat:uxx6bj254rgudk7b5fw67kw3hy

Frames and the g(k)(v) problem

Rolf Rees
1988 Discrete Mathematics  
A group divisible design (GDD) is a triple (X, 6, B) where X is a set of points, G is a partition of X into subsets (called groups) and I3 is a collection of subsets of X (called blocks) so that (i) for  ...  The quantity g@(u) denotes the smallest number of klocks required to build a pairwise balanced design on u points, given that the largest block has sixe L A well-known tiequality due to Stinson requires  ...  Take a Kirkman Triple System on 9 points (i.e. an R,RP(9,4)) (it is well known that there exist KTS(v) if and only if v = 3 mod 69 see [I] or [2] ) and Lerur~ 2. 3 . 3 Let (X, G, B) be a k-pame.  ... 
doi:10.1016/0012-365x(88)90104-5 fatcat:bocwyfxiyfhu7heytzyg3wnjry
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