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Existence of HPMDs with block size five
Author(s) -
Bennett F. E.,
Chang Y.,
Yin J.,
Zhang H.
Publication year - 1997
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1997)5:4<257::aid-jcd3>3.0.co;2-e
Subject(s) - mathematics , block size , combinatorics , block (permutation group theory) , type (biology) , group (periodic table) , block design , discrete mathematics , arithmetic , computer science , ecology , key (lock) , biology , chemistry , computer security , organic chemistry
In this article, it is shown that the necessary condition for the existence of a holey perfect Mendelsohn design (HPMD) with block size 5 and type h n , namely, n ≥ 5 and n ( n ‐ 1) h n ≡ 0 (mod 5), is also sufficient, except possibly for a few cases. The results of this article guarantee the analogous existence results for group divisible designs (GDDs) of group‐type h n with block size k = 5 and having index λ = 4. Moreover, some more conclusive results for the existence of ( v , 5, 1)‐perfect Mendelsohn designs (PMDs) are also mentioned. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 257–273, 1997