W-Complement d-Spreads, Singleton systems

The Complement of a D-Tree is Pure Shellable

W. R. D. Fairbairn

Set Systems with No Singleton Intersection

Let F be a k-uniform set system defined on a ground set of size n with no singleton intersection; i.e., no pair A,B ∈ F has |A ∩ B| = 1. Frankl showed that |F| ≤ (n−2 k−2 ) for k ≥ 4 and n sufficiently large, confirming a conjecture of Erdős and Sós. We determine the maximum size of F for k = 4 and all n, and also establish a stability result for general k, showing that any F with size asymptot...

Singleton Kinds and Singleton Types

In this dissertation I study the properties of singleton kinds and singleton types. These are extremely precise classi ers for types and values, respectively: the kind of all types equal to [a given type], and the type of all values equal to [a given value]. Singletons are interesting because they provide a very general and modular form of de nition, allow ne-grained control of type computation...

Inhibition of return spreads across 3-D space.

Focusing attention to a location in 3-D space operates much the same as in 2-D space. Attending a location in 2-D space is followed by a selective inhibitory aftereffect known as inhibition of return (IOR). Here, we report the results of two 3-D reflexive cuing studies in which depth was defined by binocular disparity. As has been shown before, attentional cuing was specific for x-y-z locations...