An existence theorem for group divisible designs of large order

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:98

Article

Mohácsy, H ; Ray-Chaudhuri, DK

关键词: group divisible designs;    transversal designs;    large order;   

DOI  :  10.1006/jcta.2001.3234

来源: Elsevier

【 摘 要 】

The following result gives a partial answer to a question of R. M. Wilson regarding the existence of group divisible designs of large order. Let k and u be positive integers, 2 less than or equal to k less than or equal to u. Then there exists an integer m(0) = m(0)(k, u) such that there exists a group divisible design of group type m(u) with block size k and index one for all integer m greater than or equal to m(0) if and only if (i) u - 1 equivalent to 0 mod(k - 1), (ii) u(u - 1) equivalent to 0 mod k(k - 1). This is a generalization of the well-known result of Chowla, Erdos, and Straus on the existence of transversal designs of large order. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free