Root cases of large sets of t-designs

Khosrovshahi, G. B.; Tayfeh-Rezaie, B.

doi:10.1016/s0012-365x(02)00574-5

Cited by 16 publications

(34 citation statements)

References 16 publications

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“…The following result gives necessary conditions on the order of these structures. This is actually a corollary to a more general result due to Khosrovshahi and Tayfeh-Rezaie [9], which gave necessary conditions on the order of large sets of t-designs. For positive integers m and n, let n [m] denote the unique integer in {0, 1, .…”

Section: History and Layout Of The Papermentioning

confidence: 60%

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Constructing regular self-complementary uniform hypergraphs

Gosselin¹

2011

J. Combin. Designs

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In this paper, we examine the possible orders of t-subset-regular selfcomplementary k-uniform hypergraphs, which form examples of large sets of two isomorphic t-designs. We reformulate Khosrovshahi and TayfehRezaie's necessary conditions on the order of these structures in terms of the binary representation of the rank k, and these conditions simplify to a more transparent relation between the order n and rank k in the case where k is a sum of consecutive powers of 2. Moreover, we present new constructions for 1-subset-regular self-complementary uniform hypergraphs, and prove that these necessary conditions are sucient for all k, in the case where t = 1.

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Section: History and Layout Of The Papermentioning

confidence: 60%

“…[9] Let t, k and n be positive integers such that t < k ≤ n. If there exists a t-subset-regular self-complementary k-hypergraph of order n, then there exists an integer a such that max{i : 2 i | k} < a ≤ min{i : 2 i > k} and n [2 a ] ∈ {t, t + 1, . .…”

Section: History and Layout Of The Papermentioning

confidence: 99%

Constructing regular self-complementary uniform hypergraphs

Gosselin¹

2011

J. Combin. Designs

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“…This assumption forces other conditions on r and s. Further results concerning the admissible parameters can be found in [7].…”

Section: Large Sets Of T-designsmentioning

confidence: 99%

“…Theorem 2.1 [7]. If there exists a LS ½Nðt; k; vÞ, then there exist LS ½Nðt À i; k À j; v À lÞ for all 0 j l i t. The following well-known extension theorems are among the important tools in constructing large sets.…”

Section: Large Sets Of T-designsmentioning

confidence: 99%

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Some results on the existence of large sets of t‐designs

Khosrovshahi

Tayfeh-Rezaie

2003

J of Combinatorial Designs

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A set of trivial necessary conditions for the existence of a large set of t-designs, LS½Nðt; k; v vÞ, isThere are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary conditions are sufficient in the cases N ¼ 2 and 3, respectively. Ajoodani-Namini has established the truth of Hartman's conjecture for t ¼ 2. Apart from this celebrated result, we know the correctness of the conjectures for a few small values of k, when N ¼ 2 and t 6, and also when N ¼ 3 and t 4. In this article, we show that similar results can be obtained for infinitely many values of k.

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Using computer software packages to enhance the teaching of engineering management science: Part 1—Critical path networks

Fulcher

Wang

2011

Comp Applic In Engineering

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The aim of this article is to share the experience of using different software packages in the delivery of critical path networks in Engineering Management Science coded as ENG4004, in the Bachelor of Engineering and Bachelor of Engineering Technology programs offered by the University of Southern Queensland (USQ), a regional Australian University with excellence in developing e-learning (Good University Guides, 2001). The article describes how the authors use different software packages to solve the critical path network problems of the course. At times, more than one package will be required for the effective delivery of a topic or module of the course. The needs for the usage were also explained. The assessments of the course were also studied and reviewed. How the software packages met the objectives of the module was also discussed together with the desired learning outcomes of students. The preferred software was Production and Operations Management (POM-QM) for Windows 3. It was finally concluded that the actual costs to the university and students are not too much but students learning experience and satisfaction will be greatly improved. ß

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Root cases of large sets of t-designs

Cited by 16 publications

References 16 publications

Constructing regular self-complementary uniform hypergraphs

Constructing regular self-complementary uniform hypergraphs

Some results on the existence of large sets of t‐designs

Using computer software packages to enhance the teaching of engineering management science: Part 1—Critical path networks

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