Block designs with repeated blocks

J.H. van Lint, H.J. Ryser

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12 Citations (Scopus)
104 Downloads (Pure)

Abstract

This paper investigates the structure of block designs with repeated blocks. Let the block design on the parameters b, v, r, k, and @l contain exactly t distinct blocks B"1, B"2, ..., B"t. Let block B"i be repeated exactly e"i times and define E =daig [e"1,...e"t]. Then the incidence matrix A of distinct blocks versus varieties satisfies the matrix equation A^TEA = (r-@l)I + @lJ, where A^T is the transpose of A, I is the indentity matrix of order v, and J is the matrix of 1's of order v. We prove that AA^T= (r-@l)E^-^1 +@lkrJ-W, where E^-^1 is the inverse of E, J is the matrix of 1's of order t, and W is a symmetric positive semidefinite matrix of order t and rank t-v. This basic relationship implies the Mann inequality e"i=
Original languageEnglish
Pages (from-to)381-396
JournalDiscrete Mathematics
Volume3
Issue number4
DOIs
Publication statusPublished - 1972

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