Design theory
Discrete Mathematics - Combinatorial designs: a tribute to Haim Hanani
Four pairwise balanced designs
Designs, Codes and Cryptography
Existence of perfect Mendelsohn designs with k=5 and &lgr;1
Discrete Mathematics
Constructions of perfect Mendelsohn designs
Discrete Mathematics
On the existence of perfect Mendelsohn designs with k=7 and &lgr; even
Discrete Mathematics
Perfect Mendelsohn designs with block size six
Discrete Mathematics
Existence of three HMOLS of types hn and 2n31
Discrete Mathematics
Pairwise Balanced Designs with Consecutive Block Sizes
Designs, Codes and Cryptography
Balanced Incomplete Block Designs with Block Size 7
Designs, Codes and Cryptography
Perfect Mendelsohn Packing Designs with Block Size Five
Designs, Codes and Cryptography
The existence of perfect Mendelsohn designs with block size 7
Discrete Mathematics
Almost resolvable perfect Mendelsohn designs with block size five
Discrete Applied Mathematics
The existence of three idempotent IMOLS
Discrete Mathematics
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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 λ v(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 λ v(v - 1)≡0 (mod 6) are sufficient except for the known impossible cases v = 6 and either λ = 2 or λ odd.