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- W2000245323 abstract "Where N is a finite set of the cardinality n and P the family of all its subsets, we study real functions on P having nonnegative differences of orders n - 2, n - 1 and n . Nonnegative differences of zeroth order, first-order, and second-order may be interpreted as nonnegativity, nonincreasingness and convexity, respectively. If all differences up to order n of a function are nonnegative, the set function is called completely monotone in analogy to the continuous case. We present a discrete Bernstein-type theorem for these functions with Möbius inversion in the place of Laplace one. Numbers of all extreme functions with nonnegative differences up to the orders n , n - 1 and n - 2, which is the most sophisticated case, and their Möbius transforms are found. As an example, we write out all extreme nonnegative nondecreasing and semimodular functions to the set N with four elements." @default.
- W2000245323 created "2016-06-24" @default.
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- W2000245323 date "1994-12-01" @default.
- W2000245323 modified "2023-09-26" @default.
- W2000245323 title "Extreme convex set functions with many nonnegative differences" @default.
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- W2000245323 doi "https://doi.org/10.1016/0012-365x(93)e0100-i" @default.
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