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Holey Steiner pentagon systems
Author(s) -
Abel R. J. R.,
Bennett F. E.,
Zhang H.
Publication year - 1999
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(1999)7:1<41::aid-jcd6>3.0.co;2-q
Subject(s) - pentagon , combinatorics , mathematics , block (permutation group theory) , type (biology) , steiner system , group (periodic table) , block size , discrete mathematics , computer science , geometry , physics , key (lock) , quantum mechanics , ecology , computer security , biology
In this article, it is shown that the necessary conditions for the existence of a holey Steiner pentagon system (HSPS) of type h n are also sufficient, except possibly for the following cases: (1) when n = 15, and h ≡ 1 or 5 (mod 6) where h ≢ 0 (mod 5), or h = 9; and (2) ( h , n ) ∈ {(6, 6), (6, 36), (15, 19), (15, 23), (15, 27), (30, 18), (30, 22), (30, 24)}. Moreover, the results of this article guarantee the analogous existence results for group divisible designs (GDDs) of type h n with block‐size k = 5 and index λ = 2. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 41–56, 1999