A UML simulator based on a generic model execution engine
Andrei Kirshin, Dany Moshkovich, et al.
ECMS 2006
Let v be a non negative integer, let λ be a positive integer, and let K and M be sets of positive integers. A group divisible design, denoted by GD[K, λ, M, v], is a triple (X, G{cyrillic}, β) where X is a set of points, G{cyrillic} = {G1, G2,...} is a partition of X, and β is a class of subsets of X with the following properties. (Members of G{cyrillic} are called groups and members of β are called blocks.) 1. 1. The cardinality of X is v. 2. 2. The cardinality of each group is a member of M. 3. 3. The cardinality of each block is a member of K. 4. 4. Every 2-subset {x, y} of X such that x and y belong to distinct groups is contained in 5. precisely λ blocks. 6. 5. Every 2-subset {x, y} of X such that x and y belong to the same group is contained in no 7. block. A group divisible design is resolvable if there exists a partition Π = {P1, P2,...} of β such that each part Pi is itself a partition of X. In this paper we investigate the existence of resolvable group divisible designs with K = {3}, M a singleton set, and all λ. The case where M = {1} has been solved by Ray-Chaudhuri and Wilson for λ = 1, and by Hanani for all λ > 1. The case where M is a singleton set, and λ = 1 has recently been investigated by Rees and Stinson. We give some small improvements to Rees and Stinson's results, and give new results for the cases where λ > 1. We also investigate a class of designs, introduced by Hanani, which we call frame resolvable group divisible designs and prove necessary and sufficient conditions for their existence. © 1989.
Andrei Kirshin, Dany Moshkovich, et al.
ECMS 2006
Anton Beloglazov, Dipyaman Banerjee, et al.
Journal of Service Research
Haim Hanani, Alan Hartman, et al.
Discrete Mathematics
Ahmed M. Assaf, Alan Hartman
Discrete Mathematics