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Special random numbers: Beyond the illusion of control

โœ Scribed by Joseph K. Goodman; Julie R. Irwin

Book ID
113829623
Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
282 KB
Volume
99
Category
Article
ISSN
0749-5978

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The interval number i(P) of a poset P is the smallest t such that P is a containment poset of sets that are unions of at most t real intervals. For the special poset Bn(k) consisting of the singletons and k-subsets of an n-element set, ordered by inclusion, i(B~(k))---min{k,nk + 1} if In~2-kl >~ n/2

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For a pair of integers 1 F โฅr, the โฅ-chromatic number of an r-uniform ลฝ . hypergraph H s V, E is the minimal k, for which there exists a partition of V into subsets < < T, . . . , T such that e l T F โฅ for every e g E. In this paper we determine the asymptotic 1 k i ลฝ . behavior of the โฅ-chromatic n