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On the existence of mandatory representation designs with block sizes 3 and k
Author(s) -
Grüttmüller Martin
Publication year - 2000
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(2000)8:2<122::aid-jcd4>3.0.co;2-3
Subject(s) - mathematics , block (permutation group theory) , combinatorics , representation (politics) , block design , arithmetic , law , political science , politics
A mandatory representation design MR [ν, K ] is a pairwise balanced design on ν points with block sizes from K in which for each k ∈ K there is a block in the design of size k . Mendelsohn and Rees [4] investigated the existence of MR [ν, K ]s, where 3 ∈ K . In this report we consider additional necessary conditions, where K = {3, k }. These conditions are proved to be sufficient for 4 ≤ k ≤ 50 with one genuine exception. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 122–131, 2000