A note on GDD(1, n, n, 4; λ_1, λ_2)

  • Dinesh G. Sarvate
  • Dinkayehu M. Woldemariam Adama Science and Technology University
Keywords: $t$-designs, Group divisible designs with unequal group sizes, BIBDs

Abstract

The present note is motivated by two papers on group divisible designs (GDDs) with the same block size three but different number of groups: three and four where one group is of size $1$ and the others are of the same size $n$. Here we present some interesting constructions of GDDs with block size 4 and three groups: one of size $1$ and other two of the same size $n$. We also obtain necessary conditions for the existence of such GDDs and prove that they are sufficient in several cases. For example, we show that the necessary conditions are sufficient for the existence of a GDD$(1,n,n,4;\lambda_1,\lambda_2)$ for $n\equiv0,1,4,5,8,9\pmod{12}$ when $\lambda_1\ge \lambda_2$.

Author Biography

Dinkayehu M. Woldemariam, Adama Science and Technology University

Ph.D. student

References

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A. Sakda, C. Uiyyasathian, Group divisible designs GDD$(n,n,n,1;lambda_1,lambda_2)$, Australas. J. Comb. 69(1) (2017) 18–28.

Published
2022-04-30
Section
Articles