Forbidden subposets for fractional weak discrepancy at most k

2009/8/28 Friday 4PM-5PM

The fractional weak discrepancy of a poset (partially ordered set) P, written wd(P), is the least k such that some \(f:P\to\mathbb{R}\) satisfies f(y)-f(x)≤1 for \(x\prec y\) and |f(y)-f(x)|≤k for x|y. Minimal forbidden subposets are often called *obstructions*. Shuchat, Shull, and Trenk determined the obstructions for the property wd(P)<1: the obstructions are **2**+**2** and **3**+**1**. We determine the obstructions for the property wd(P)≤k when k is an integer. In this talk, the complete collection of the obstructions for wd(P)≤k for each k≥2 – which is an infinite set – will be discussed.

This is joint work with Douglas B. West.