The Kruskal-Katona Theorem and a Characterization of System Signatures
نویسندگان
چکیده
منابع مشابه
The Kruskal-Katona Theorem and a Characterization of System Signatures
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 and Katona. We also show how the same appr...
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A bound on consecutive clique numbers of graphs is established. This bound is evaluated and shown to often be much better than the bound of the Kruskal-Katona theorem. A bound on non-consecutive clique numbers is also proven.
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As we have seen, antichains and intersecting families are fundamental to Extremal Set Theory. The two central theorems, Sperner’s Theorem and the Erdős–Ko–Rado Theorem, have inspired decades of research since their discovery, helping establish Extremal Set Theory as a vibrant and rapidly growing area of Discrete Mathematics. One must, then, pay a greater than usual amount of respect to the Krus...
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2015
ISSN: 0021-9002,1475-6072
DOI: 10.1239/jap/1437658612