engleski

Construction of 1-designs from group action

Let G be a finite group acting on sets Ω and Ω′. Denote the orbits of those actions by Ω1, ..., Ωk and Ω′1, ..., Ω′k′. One can construct a transitive 1−design with |Ωi|, i=1, ..., k, points and |Ω′j|, j= 1, ..., k′, blocks (or |Ωi|, i= 1, ..., k, blocks and |Ω′j|, j=1, ..., k′, points) whose base block is ∪_{;i=1};^s Gα.βi, α∈Ωj, β1, ..., βs ∈ Ωi. Combining incidence matrices of those transitive 1−designs we construct an incidence matrix of a non-transitive design.

design; orbit matrix; group action; transitive design; primitive design

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