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Large sets of coverings
Author(s) -
Etzion Tuvi
Publication year - 1994
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.3180020509
Subject(s) - disjoint sets , mathematics , combinatorics , context (archaeology) , dual (grammatical number) , space (punctuation) , disjoint union (topology) , upper and lower bounds , discrete mathematics , computer science , mathematical analysis , art , paleontology , literature , biology , operating system
Large sets of packings were investigated extensively. Much less is known about the dual problem, i.e., large sets of coverings. We examine two types of important questions in this context; what is the maximum number of disjoint optimal coverings? and what is the minimum number of optimal coverings for which the union covers the space? We give various constructions which give the optimal solutions and some good upper and lower bounds on both questions, respectively. © 1994 John Wiley & Sons, Inc.