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Existence of large sets of coverings with block size 3
Author(s) -
Ji L.
Publication year - 2006
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.20077
Subject(s) - mathematics , disjoint sets , combinatorics , block (permutation group theory) , class (philosophy) , order (exchange) , discrete mathematics , computer science , finance , artificial intelligence , economics
Two types of large sets of coverings were introduced by T. Etzion (J Combin Designs, 2(1994), 359–374). What is maximum number (denoted by λ( n,k )) of disjoint optimal ( n,k,k − 1) coverings? What is the minimum number (denoted by µ( n,k )) of disjoint optimal ( n,k,k − 1) coverings for which the union covers the space? For k = 3, the numbers µ( n,k ) have been determined with an unsolved order n = 17, and the numbers λ( n,k ) have also been determined with an unsolved infinite class n ≡ 5 (mod 6). The unsolved numbers λ( n ,3) and µ(17,3) will be completed in this note. This solution is based on the existence of a class of partitionable candelabra systems. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 400–405, 2006