Abstract
We prove imbedding theorems for block designs balanced with respect to pairs, and with the aid of these theorems we establish the existence of (v, k, λ)-resolvable BIB block designs with parameters v, k, λ such that λ=k−1 [and also such that λ=(k−l)/2 if k is odd], k ¦(p−1) for each prime divisor p of the number v/k; we also establish an imbedding theorem for Kirkman triple systems.
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Translated from Matematicheskie Zametki, Vol. 16, No. 1, pp. 173–184, July, 1974.
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Rumov, B.T. Some imbedding theorems for block designs balanced with respect to pairs. Mathematical Notes of the Academy of Sciences of the USSR 16, 686–692 (1974). https://doi.org/10.1007/BF01098827
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DOI: https://doi.org/10.1007/BF01098827