#### Department

Computer Science, Mathematics

#### Document Type

Article

#### Publication Date

4-2011

#### Abstract

The *fractional weak discrepancy *wd_{F}(P) of a poset P=(V,≺) was introduced in Shuchat et al. (2007) [6] 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 Shuchat et al. (2006, 2009) [5] and [7] on the range of wd_{F} 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.

#### Recommended Citation

Shuchat, A., Shull, R., & Trenk, A. N. (2011). Fractional Weak Discrepancy and Split Semiorders. Discrete Applied Mathematics, 159(7): 647-660. doi:10.1016/j.dam.2010.04.014

#### Version

Post-print

## Comments

Post-print version, Nov. 8, 2010. Published version in: Discrete Applied Mathematics, 159(7): 647-660 (2011). doi:10.1016/j.dam.2010.04.014