June 2015 The Kruskal-Katona theorem and a characterization of system signatures
Alessandro D'Andrea, Luca De Sanctis
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J. Appl. Probab. 52(2): 508-518 (June 2015). DOI: 10.1239/jap/1437658612

Abstract

We show how to determine if a given vector can be the signature of a system on a finite number of components and, if so, exhibit such a system in terms of its structure function. The method employs combinatorial results from the theory of (finite) simplicial complexes, and provides a full characterization of signature vectors using a theorem of Kruskal (1963) and Katona (1968). We also show how the same approach can provide new combinatorial proofs of further results, e.g. that the signature vector of a system cannot have isolated zeroes. Finally, we prove that a signature with all nonzero entries must be a uniform distribution.

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Alessandro D'Andrea. Luca De Sanctis. "The Kruskal-Katona theorem and a characterization of system signatures." J. Appl. Probab. 52 (2) 508 - 518, June 2015. https://doi.org/10.1239/jap/1437658612

Information

Published: June 2015
First available in Project Euclid: 23 July 2015

zbMATH: 1360.94305
MathSciNet: MR3372089
Digital Object Identifier: 10.1239/jap/1437658612

Subjects:
Primary: 60C05
Secondary: 93E03

Keywords: reliability , signature , simplicial complexes

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 2 • June 2015
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