On Derivation of Initial Blocks of B.I.B. Designs With More Than One Initial Block

Das, Moumita; Kulshreshtha, A. C.

doi:10.1111/j.1467-842x.1968.tb00217.x

Cited by 5 publications

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“…Given Theorem 4 was proved by Das and Kulshreshtha [2] under the redundant restriction that the first design is obtained by the method of difference.…”

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confidence: 98%

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Coexistence of some B.I.B. Designs

Majindar

1978

Can. math. bull.

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“…Given Theorem 4 was proved by Das and Kulshreshtha [2] under the redundant restriction that the first design is obtained by the method of difference.…”

Section: •»©mentioning

confidence: 98%

“…Similarly there are r-k other varieties which occur in B q , none of which occurs in B p . So corresponding to case (i), there are (r-k) 2 columns, the intersections of each of which with the pth and qth rows of A have 1 as entries.…”

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confidence: 99%

Coexistence of some B.I.B. Designs

Majindar

1978

Can. math. bull.

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“…result for a derivation of initial blocks generating BIB designs in [3]. In this note Lemma 3 is shown to be false.…”

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confidence: 87%

“…Some of the discussion of the second method of constructing a BIB design in [3] must be changed. Particularly, the Lemma in Section 3 of [3] and the arguments which nse this Lemma.…”

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confidence: 99%

A NOTE ON BIB DESIGNS¹

Kageyama

Ishu

1975

Australian Journal of Statistics

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On supplementary difference sets

Wallis

1972

Aeq. Math.

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Given a finite abelian group V a n d subsets $1, Sz, ..., Sn of V, write T~ for the totality of all the possible differences between elements of S~ (with repetitions counted multiply) and T for the totality of members of all the T~. If T contains each non-zero eJement of V the same number of times, then the sets $1, $2 ..... S, will be called supplementary difference sets.We discuss some properties for such sets, give some existence theorems and observe their use in the construction of Hadamard matrices and balanced incomplete block designs. DefinitionsSuppose V is a finite abelian group with v elements, written in additive notation. A difference set D with parameters (v, k, ).) is a subset of V with k elements and such that in the totality of all the possible differences of elements from D each non-zero element of V occurs 2 times.If V is the set of integers modulo v then D may be called a cyclic difference set: these are extensively discussed in Baurnert [1].It is often easier to discuss a subset D of an abelian group in terms of its incidence matrix A = (aij) which is obtained by ordering the elements of V as v,, v2,..., v v in some way and then choosing 0 i = j a~j = + 1 (vj--v~ Throughout the remainder of this paper I will always mean the identity matrix and J the matrix with every element + 1, where the order, unless specifically stated, is determined by the context.Although there are many equivalent definitions, we define a (v, k, 2)-configuration to be a (0, 1)-matrix A of order v, with row and column sum k, such that the inner product of any two row vectors is 4. Hence A satisfies A A r = (k -A) I + JlJ.

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On Derivation of Initial Blocks of B.I.B. Designs With More Than One Initial Block

Abstract: A table of difference sets generating balanced incomplete Rev. I& Statist. Inst., 30,[361][362][363][364][365][366]

Cited by 5 publications

References 3 publications

Coexistence of some B.I.B. Designs

Coexistence of some B.I.B. Designs

A NOTE ON BIB DESIGNS¹

On supplementary difference sets

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On Derivation of Initial Blocks of B.I.B. Designs With More Than One Initial Block

Abstract: A table of difference sets generating balanced incomplete Rev. I& Statist. Inst., 30,[361][362][363][364][365][366]

Cited by 5 publications

References 3 publications

Coexistence of some B.I.B. Designs

Coexistence of some B.I.B. Designs

A NOTE ON BIB DESIGNS1

On supplementary difference sets

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A NOTE ON BIB DESIGNS¹