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On 1-Sarvate–Beam designs
2011
Discrete Mathematics
The solution to a set theory exercise, "Partition the set of positive integers {1, 2, . . . , v} into k subsets such that the sum of the elements in each subset is v(v + 1)/(2k) whenever v(v + 1)/(2k) is an integer", gives a construction of non-simple 1-SB designs. This raises a natural question of the existence of simple 1-SB designs. We show that the necessary conditions for the existence of simple 1-SB designs for block sizes 2, 3, 4, 5 and 6 are sufficient. Moreover, the technique exhibited
doi:10.1016/j.disc.2011.02.004
fatcat:hxynvf23cvfnnjwx2ea3gijiim