Vol. 64, No. 2, 1976

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Construction of 2-balanced (n,k,λ) arrays

Frank Kwang-Ming Hwang and Shen Lin

Vol. 64 (1976), No. 2, 437–453

Let In denote the set of positive integers {1,2,,n}, and Inλ the multiset consisting of λ copies of In. A submultiset S of Inλ is t-balanced if S can be partitioned into t parts such that the sums of all elements in each part are all equal. A t-balance (n,k,λ) array is a partition of Inλ into m multisets Si, i = 1,,m, which are all of size k and t-balanced. In this paper, we give a necessary and sufficient condition for the existence of 2-balanced (n,k,λ) arrays. Furthermore, we show how 2-balanced (n,k,λ) arrays can be used to construct a class of neighbor designs used in serology, or to give coverings of complete multigraphs by k-cycles.

Mathematical Subject Classification 2000
Primary: 05B30
Received: 1 March 1974
Published: 1 June 1976
Frank Kwang-Ming Hwang
Shen Lin