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On large sets of Kirkman triple systems and 3-wise balanced design
2004
Discrete Mathematics
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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
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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
2002
Discrete Mathematics
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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
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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
2008
Discrete Mathematics
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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
2009
Discrete Mathematics
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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
1988
Journal of the Australian Mathematical Society
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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
2002
Discrete Mathematics
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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
2014
IEEE Transactions on Information Theory
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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]
2013
arXiv
pre-print
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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
2005
Journal of combinatorial theory. Series A
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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
2000
Discrete Applied Mathematics
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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
2009
Mathematica Slovaca
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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
2009
Discrete Mathematics
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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
1988
Discrete Mathematics
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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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