Fractional weak discrepancy and split semiorders
نویسندگان
چکیده
The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) was introduced in [5] as the minimum nonnegative k for which there exists a function f : V → R satisfying (i) if a ≺ b then f(a)+1 ≤ f(b) and (ii) if a ‖ b then |f(a) − f(b)| ≤ k. In this paper we generalize results in [6, 7] on the range of wdF for semiorders to the larger class of split semiorders. In particular, we prove that for such posets the range is the set of rationals that can be represented as r/s for which 0 ≤ s− 1 ≤ r < 2s.
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 159 شماره
صفحات -
تاریخ انتشار 2011