Existence of HPMDs with block size five

Bennett, F. E.; Chang, Yanxun; Yin, Jianxing; Zhang, H.

doi:10.1002/(sici)1520-6610(1997)5:4<257::aid-jcd3>3.0.co;2-e

J. Combin. Designs

1997

DOI: 10.1002/(sici)1520-6610(1997)5:4<257::aid-jcd3>3.0.co;2-e

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Existence of HPMDs with block size five

F. E. Bennett

Yanxun Chang

Jianxing Yin³

et al.

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Cited by 12 publications

References 9 publications

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Super‐simple holey Steiner pentagon systems and related designs

Abel

Bennett

2007

J of Combinatorial Designs

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A Steiner pentagon system of order v (SPS(v)) is said to be super-simple if its underlying (v, 5, 2)-BIBD is super-simple; that is, any two blocks of the BIBD intersect in at most two points. It is well known that the existence of a holey Steiner pentagon system (HSPS) of type T implies the existence of a (5, 2)-GDD of type T. We shall call an HSPS of type T super-simple if its underlying (5, 2)-GDD of type T is super-simple; that is, any two blocks of the GDD intersect in at most two points. The existence of HSPSs of uniform type h n has previously been investigated by the authors and others. In this article, we focus our attention on the existence of super-simple HSPSs of uniform type h n .

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Super‐simple holey Steiner pentagon systems and related designs

Abel

Bennett

2007

J of Combinatorial Designs

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Existence of 4-fold perfect (v, {5, 8}, 1)-Mendelsohn designs

Xiang

Bennett

2010

Acta. Math. Sin.-English Ser.

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The Existence of (ν,6, λ)-Perfect Mendelsohn Designs with λ > 1

Abel

Bennett

2006

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The basic necessary conditions for the existence of a (v, k, λ)-perfect Mendelsohn design (briefly (v, k, λ)-PMD) are v ≥ k and λv(v − 1) ≡ 0 (mod k). These conditions are known to be sufficient in most cases, but certainly not in all. For k = 3, 4, 5, 7, very extensive investigations of (v, k, λ)-PMDs have resulted in some fairly conclusive results. However, for k = 6 the results have been far from conclusive, especially for the case of λ = 1, which was given some attention in papers by Miao and Zhu [34], and subsequently by Abel et al. [1]. Here we investigate the situation for k = 6 and λ > 1. We find that the necessary conditions, namely v ≥ 6 and λv(v − 1) ≡ 0 (mod 6) are sufficient except for the known impossible cases v = 6 and either λ = 2 or λ odd.Keywords Perfect Mendelsohn design · Incomplete Perfect Mendelsohn design · Holey Perfect Mendelsohn design · GDD · PBD

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Existence of HPMDs with block size five

Cited by 12 publications

References 9 publications

Super‐simple holey Steiner pentagon systems and related designs

Super‐simple holey Steiner pentagon systems and related designs

Existence of 4-fold perfect (v, {5, 8}, 1)-Mendelsohn designs

The Existence of (ν,6, λ)-Perfect Mendelsohn Designs with λ > 1

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