E-viri
PDF
Recenzirano
Odprti dostop
-
Shuchat, Alan; Shull, Randy; Trenk, Ann N.
Discrete Applied Mathematics, 04/2011, Letnik: 159, Številka: 7Journal Article
The fractional weak discrepancy w d 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) 5,7 on the range of w d 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 < 2 s .
