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Range Of The Fractional Weak Discrepancy Function, Alan Shuchat, Randy Shull, Ann N. Trenk
Range Of The Fractional Weak Discrepancy Function, Alan Shuchat, Randy Shull, Ann N. Trenk
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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 wdF (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 wdF is the set of rational numbers …