期刊
JOURNAL OF SYMBOLIC COMPUTATION
卷 44, 期 9, 页码 1311-1325出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsc.2008.06.002
关键词
Multi-state reliability; Coherent systems; Monomial ideals; Betti numbers; Multigraded Hilbert series; Mayer-vietoris trees
Every coherent system has a monomial ideal associated with it and the knowledge of its multigraded Betti numbers provides reliability bounds for the corresponding system, which are the tightest among a certain class of such bounds. Some alternative methods for computing the multigraded Betti numbers are used in this paper and applied in the study of reliability. We obtain special results for well known examples and show that computational commutative algebra techniques can be used beneficially in the reliability analysis of systems of different types. (C) 2009 Elsevier Ltd. All rights reserved.
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