Range of the Fractional Weak Discrepancy Function

Alan Shuchat; Randy Shull; Ann N. Trenk

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Range of the Fractional Weak Discrepancy Function

机译：分数弱差异函数的范围

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In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset and characterize semiorders in terms of these values. In [6], we defined the fractional weak discrepancy wd_F(P) of a poset P = (V, < ) to be the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a < b then f(a) + 1 ≤ f(b) and (2) if a‖b then | f(a)-f(b)| ≤ k. This notion builds on previous work on weak discrepancy in [3, 7, 8]. We prove here that the range of values of the function wd_F is the set of rational numbers that are either at least one or equal to r/(r+1) for some nonnegative integer r. Moreover, P is a semiorder if and only if wd_F(P) < 1, and the range taken over all semiorders is the set of such fractions r/(r+1).

机译：在本文中，我们描述了一个姿势的分数弱差异所能取的值的范围，并根据这些值来表征半阶。在[6]中，我们定义了位姿P =（V，<）的分数弱差异wd_F（P）为存在函数f的最小非负k：如果a

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来源
《Order》 |2006年第1期|p.51-63|共13页
作者
Alan Shuchat; Randy Shull; Ann N. Trenk;
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作者单位

Department of Mathematics, Wellesley College, Wellesley, MA 02481, USA;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
weak discrepancy; fractional weak discrepancy; weak orders; semiorders;

机译：弱差异;分数弱差异;弱阶;半阶;

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Range of the Fractional Weak Discrepancy Function

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