✍ Scribed by H. Cao
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A (k,λ)‐semiframe of type g^u^ is a (k,λ)‐group‐divisible design of type g^u^ (𝒳, 𝒢, ℬ︁), in which the collection of blocks ℬ︁ can be written as a disjoint union ℬ︁=𝒫∪ℒ︁ where ℒ︁ is partitioned into parallel classes of 𝒳 and 𝒫 is partitioned into holey parallel classes, each holey parallel class being a partition of 𝒳_G_~j~ for some G~j~∈𝒢. In this paper, we shall prove that the necessary conditions for (3,λ)‐semiframes of type 3__^u^__ are also sufficient with one exception. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 253–265, 2009
📜 SIMILAR VOLUMES
In this article, we investigate the existence of pure (v,4,A)-PMD with A = 1 and 2, and obtain the following results: (1) a pure (v, 4,1)-PMD exists for every positive integer Y = 0 or 1 (mod 4) with the exception of v = 4 and 8 and the possible exception of v = 12; (2) a pure (v,4,2)-PMD exists for
In this article, we describe some new constructions for Room frames and use them to show the existence of Room frames of types t 4 and t s . Combining the result with those of Dinitz and Stinson leads to the following: the only cases for which the existence of Room frames is undecided are those type