Some results on the existence or nonexistence of constant block-sum triangular and other related designs. (English) Zbl 07618101
Summary: We discuss issues pertaining to existence or nonexistence of triangular designs with constant block-sum property as previously introduced by R. Khattree. The problem has two aspects: the quantitative treatments must be equally spaced or treatments do not have to be equally spaced, and the levels of these treatments are to be determined by the design itself. The incidence matrix and the eigen properties of the corresponding concurrence matrix play a critical role in this investigation. In the process of developing results, we also observe connections between constant block-sum property of the partially balanced incomplete block designs with some associated balanced incomplete block designs.
Keywords:
constant block-sum partially balanced incomplete block designs; incidence matrix; partially balanced incomplete block designs; triangular designs; group divisible designsReferences:
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