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On the Spectrum of Steiner (v,k,t) Trades (II)

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Abstract.

 A (v,k,t) trade T=T 1T 2 of volume m consists of two disjoint collections T 1 and T 2 each containing m blocks (k-subsets) such that each t-subset is contained in the same number of blocks in T 1 and T 2. If each t-subset occurs at most once in T 1, then T is called a Steiner (k,t) trade. In this paper, we continue our investigation of the spectrum S(k,2); that is, the set of allowable volumes of Steiner (k,t) trades when t=2. By using the concept of linked trades, we show that 2k+1∈S(k,2) precisely when k∈{3, 4, 7}.

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Received: February 28, 1997

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Gray, B., Ramsay, C. On the Spectrum of Steiner (v,k,t) Trades (II). Graphs Comb 15, 405–415 (1999). https://doi.org/10.1007/s003730050074

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  • DOI: https://doi.org/10.1007/s003730050074

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