Forbidden subposets for fractional weak discrepancy at most

The fractional weak discrepancy of a poset P , written wd F ( P ) , is the least k such that some f : P → R satisfies f ( y ) − f ( x ) ≥ 1 for x ≺ y and | f ( y ) − f ( x ) | ≤ k for x ∥ y . We determine the minimal forbidden subposets for the property wd F ( P ) ≤ k when k is an integer.