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Finiteness Results in Triangle‐Free Quasi‐Symmetric Designs
Author(s) -
Pawale Rajendra M.
Publication year - 2013
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.21320
Subject(s) - mathematics , combinatorics , intersection (aeronautics) , isosceles triangle , discrete mathematics , geometry , engineering , aerospace engineering
Abstract Triangle‐free quasi‐symmetric 2‐ ( v , k , λ ) designs with intersection numbers x , y ; 0 ≤ x ≤ y ≤ k and λ > 1 are investigated. Possibility of triangle‐free quasi‐symmetric designs with λ = 2 y or k − x = 3 ( y − x ) is ruled out. It is also shown that, for a fixed x and a fixed ratio ( k − x ) / ( y − x ) ≥ 3 , there are only finitely many triangle‐free quasi‐symmetric designs. © 2012 Wiley Periodicals, Inc. J Combin Designs 00: 1‐6, 2012