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Some imbedding theorems for block designs balanced with respect to pairs

Research paper by B. T. Rumov

Indexed on: 01 Jul '74Published on: 01 Jul '74Published in: Mathematical Notes



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.