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Transverse quadruple systems with five holes
Author(s) -
Keranen M. S.,
Kreher D. L.
Publication year - 2007
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/jcd.20114
Subject(s) - mathematics , combinatorics , type (biology) , transverse plane , ecology , structural engineering , engineering , biology
Transverse Steiner quadruple systems with five holes are either of type g 5 or g 4 u 1 . We concentrate on the systems of type g 4 u 1 and settle existence except when g ≡ u ≡ 2 (mod 4) and all except 40 parameter situations when g ≡ u + 2 ≡ 0 (mod 4). The question of existence for transverse quadruple systems of type g 4 u 1 with index λ > 1 is completely solved for all λ ≥ 13 and λ ∈ {4, 6, 8, 9, 10, 12}. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 315–340, 2007