On Non-existence of Affine αresolvable Triangular Designs
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The existence on affine αresolvability with some properties has been discussed for block designs in literature since 1942 for a =1 and in particular since 1963 for a ≥ 2. Recently, Kageyama (2007) disproved the validity of such concept for regular group divisible designs. A similar problem for 2-associate triangular designs will be tackled here. No example has been found for an affine αresolvable triangular design for any a in literature. In this paper, when a = 1,2, the non-existence of an affine αresolvable triangular design will be shown completely, whereas, when a ≥ 3, partial non-existence results are provided.
AMS Subject Classification: Primary 62K10, Secondary 05B05.
Keywordstriangular design αresolvable affine αresolvable
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