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October 6 Math Colloquium

Dinesh Sarvate, CofC

Progress towards new concept in Group Divisible Designs.

We extend the definitions of a group divisible design and a t-design and define a 3-GDD(n,2,k,λ12) and give some necessary conditions for its existence. We show that the conditions are sufficient for the existence of a 3-GDD(n, 2, 4.λ1, λ2) except possibly when n ≡ 1,3 (mod 6), n≠ 3,7,13 and λ1 > λ2. It is known that a large set for 7 (partition of all 3-subsets of a 7-set into 5 Steiner triple systems (STSs)) does not exist, but we show that the collection of all 3-sets of a 7-set along with a STS on the 7-set can be partitioned into 6 STSs.

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