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Some results on the existence of large sets of t‐designs
Author(s) -
Khosrovshahi G. B.,
TayfehRezaie R.
Publication year - 2003
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.10027
Subject(s) - conjecture , mathematics , correctness , combinatorics , set (abstract data type) , state (computer science) , discrete mathematics , algorithm , computer science , programming language
Abstract A set of trivial necessary conditions for the existence of a large set of t ‐designs, LS [N]( t,k, ν), is $N\big | {{\nu \hskip -3.1 \nu}-i \choose k-i}$ for i = 0,…, t . There are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary conditions are sufficient in the cases N = 2 and 3, respectively. Ajoodani‐Namini has established the truth of Hartman's conjecture for t = 2. Apart from this celebrated result, we know the correctness of the conjectures for a few small values of k , when N = 2 and t ≤ 6, and also when N = 3 and t ≤ 4. In this article, we show that similar results can be obtained for infinitely many values of k . © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 144–151, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10027