Results 181 to 190 of about 68,154 (212)
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Ars Comb., 2017
The paper presents two constructions of PBIB designs with two classes of treatments that sometimes yield a BIB design. Treatments are in both constructions identified with unordered pairs of elements from a fixed set. Treatments can be thus regarded as edges of a complete graph, and thus one gets a class of pairs of edges that intersect, and a class of
Roger Logan +2 more
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The paper presents two constructions of PBIB designs with two classes of treatments that sometimes yield a BIB design. Treatments are in both constructions identified with unordered pairs of elements from a fixed set. Treatments can be thus regarded as edges of a complete graph, and thus one gets a class of pairs of edges that intersect, and a class of
Roger Logan +2 more
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A note on BIB designs with nested rows and columns [PDF]
Australas. J Comb., 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
James Arthur MacDougall, Gary L. Mullen
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A class of BIB designs with repeated blocks
Journal of Applied Statistics, 2001Balanced incomplete block design (BIBD) with repeated blocks is studied in detail. Methods of construction of BIB designs with repeated blocks are developed so as to distinguish the usual BIBD and BIBD with repeated blocks. One additional parameter, say d, is considered here, where d denotes the number of distinct blocks present in the BIB design with ...
D. K. Ghosh, S. B. Shrivastava
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Cyclic resolutions of the BIB design in PG(5, 2) [PDF]
Australas. J Comb., 2020 It is shown that a BIB design generated by points and planes in \(\text{PG}(5, 2)\) has two types of automorphisms, i.e., a cyclic one of order \(2^6-1\) and a \(2\)-rotational one of order \(2^5-1\). These designs are also cyclically resolvable. The argument is based on a computer search.
Takaaki Hishida, Masakazu Jimbo
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Difference families, difference matrices, and bib-designs
Mathematical Notes of the Academy of Sciences of the USSR, 1985The author continues his work on difference families in additive Abelian groups of finite orders [For earlier works see Mat. Sb., Nov. Ser. 99(141), 366-379 (1976; Zbl 0405.05010), and Mat. Zametki 32, No.6, 869- 887 (1982; Zbl 0506.05011)]. The present paper contains many interesting construction theorems.
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A new series of \(\mu\)-resolvable BIB designs [PDF]
, 2002 Summary: A method of constructing a series of \(\mu\)-resolvable BIB designs from mutually orthogonal mates of BIB designs is provided. The resolvable designs obtainable through this method are new and involve lesser number of blocks for a fixed number of treatments than those obtained by \textit{S. Kageyama} and \textit{R. N. Mohan} [Discrete Math. 45,
Kageyama, Sanpei +2 more
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Bib Designs with Blocks of Maximal Multiplicity.
1982Abstract : The set of distinct blocks of a block design is known as its support. We construct a BIB design with parameters V or = 7, k = 3, lambda = v - 2 which contains a block of maximal multiplicity and has support (V/3) - 4(v-3). Any BIB design which contains such a block and has parameters as above must be supported on at most (V/3) - 4(v-3 ...
A. S. Hedaya, G. M. Constantine
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On the existence of BIB designs with large λ
Journal of Statistical Planning and Inference, 2001Abstract In this article we prove the following theorem: Suppose that v and k are given, v⩾k+2 and λ 0 (v,k)=( v−2 k−2 ) 2 ·4 v−k−1 . If λ(v−1)≡0 ( mod k−1) , λv(v−1)≡0 ( mod k(k−1)) and λ>λ0(v,k), then there is a B(v,k,λ).
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A study of BIB designs through support matrices
Journal of Statistical Planning and Inference, 1985The algebraic approach for studying BIB designs with repeated blocks, introduced by \textit{W. Foody} and \textit{A. Hedayat} [Ann. Stat. 5, 932-945 (1977; Zbl 0368.62054)] is further developed. The concept of a support matrix is introduced, and the connection between full column rank support matrices and irreducible designs is explored.
Hedayat, A., Pesotan, H.
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Biometrical Journal, 1980
AbstractIn addition to the first part we prove independently of the model some theorems on properties of balanced block designs. Then we propose nine methods of construction of BIB and prove theorems in connection with these methods. In a table we give a survey on block designs with v$25 and possibilities of their construction with these methods ...
Rasch, D., Herrendörfer, G.
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AbstractIn addition to the first part we prove independently of the model some theorems on properties of balanced block designs. Then we propose nine methods of construction of BIB and prove theorems in connection with these methods. In a table we give a survey on block designs with v$25 and possibilities of their construction with these methods ...
Rasch, D., Herrendörfer, G.
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