Fractional weak discrepancy and split semiorders Original Research Article

The fractional weak discrepancy image of a poset image was introduced in Shuchat et al. (2007) as the minimum nonnegative image for which there exists a function image satisfying (i) if image then image and (ii) if image then image. In this paper we generalize results in Shuchat et al. (2006, 2009) on the range of image 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 image for which image.