The fractional weak discrepancy of a partially ordered set

Authors:
Alan Shuchat;Randy Shull;Ann N. Trenk
Affiliations:
Department of Mathematics, Wellesley College, Wellesley, MA 02481, USA;Department of Compute Science, Wellesley College, Wellesley, MA 02481, USA;Department of Mathematics, Wellesley College, Wellesley, MA 02481, USA
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 4
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Abstract

In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [J.G. Gimbel and A.N. Trenk, On the weakness of an ordered set, SIAM J. Discrete Math. 11 (1998) 655-663; P.J. Tanenbaum, A.N. Trenk, P.C. Fishburn, Linear discrepancy and weak discrepancy of partially ordered sets, ORDER 18 (2001) 201-225; A.N. Trenk, On k-weak orders: recognition and a tolerance result, Discrete Math. 181 (1998) 223-237]. The fractional weak discrepancywd"F(P) of a poset P=(V,@?) is the minimum nonnegative k for which there exists a function f:V-R satisfying (1) if a@?b then f(a)+1=