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- W2053887948 abstract "Abstract An ( r , 1) system is pair ( V, F ) where V is a v -set and F is a family of non-null subsets of V (b in number) which satisfy the following. (i) Every pair of distinct members of V occur in precisely one member of F ; (ii) Every member of V occurs in precisely r members of F . A pseudo parallel complement PPC(n, α) is an ( n +1, 1) system with ν = n 2 – αn and b ≦ n 2 + n – α in which there are at least n – α blocks of size n . A pseudo intersection complement PIC (n, α) is an ( n +1, 1) system with ν= n 2 – αn + α – 1 b ≦ n 2 +n – α in which there are at least n – α +1 blocks of size n-1 . It is shown that for α ≧ 4, every PIC (n, α) can be embedded in a PPC(n, α – 1) and that for n > (α 4 + 2α 3 + 2α 2 + α)/2 every PPC (n, α) can be embedded in a projective plant of order n . The latter generalizes a result of Totten (who proves the result for α = 1)." @default.
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- W2053887948 date "1976-12-01" @default.
- W2053887948 modified "2023-09-26" @default.
- W2053887948 title "A generalization of a theorem of Totten" @default.
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- W2053887948 doi "https://doi.org/10.1017/s1446788700016360" @default.
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