The existence of some resolvable block designs with divisibility into groups |
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Authors: | B T Rumov |
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Institution: | (1) V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Moscow |
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Abstract: | This paper proves the existence of resolvable block designs with divisibility into groups GD(v; k, m; 1, 2) without repeated blocks and with arbitrary parameters such that 1 = k, (v–1)/(k–1) 2 vk–2 (and also 1 k/2, (v–1)/(2(k–1)) 2 vk–2 in case k is even) k 4 andp=1 (mod k–1), k < p for each prime divisor p of number v. As a corollary, the existence of a resolvable BIB-design (v, k, ) without repeated blocks is deduced with X = k (and also with = k/2 in case of even k) k
, where a is a natural number if k is a prime power and=1 if k is a composite number.Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 623–634, April, 1976. |
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