2009 N 1 16 ๚: |
uาFๅe น (LๅEwคศ)
uฺ่FExistence of affine α-resolvable PBIB designs with some constructions
A mathematical topic using the property of resolvability and
affine resolvability was introduced in 1850 and the designs having such
concept have been statistically discussed since 1939. Their combinatorial
structure on existence has been discussed richly since 1942. This concept
was generalized to α-resolvability and affine α-resolvability in 1963.
These arguments are mostly done for a class of balanced incomplete block
designs. The present paper will make the combinatorial investigation on
affine α-resolvable partially balanced incomplete block designs with two
associate classes. The characterization of parameters in a closed form will
be given and then existence problems with construction methods will be
discussed. Comprehensive and useful results on combinatorics are obtained.
Several methods of construction are newly presented with some illustrations.