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We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in R d is contained in at least (d + 2) 2 /4 simplices with one vertex from each set. Given a set S of points in R d and an additional point p, the simplicial depth of p with respect to S, denoted depth S (p), is the number of closed d-simplices generated from points of S… (More)

It is known that a graded lattice of rank n is supersolvable if and only if it has an EL-labelling where the labels along any maximal chain are exactly the numbers 1, 2,. .. , n without repetition. These labellings are called Sn EL-labellings, and having such a labelling is also equivalent to possessing a maximal chain of left modular elements. In the case… (More)

The usual, or type An, Tamari lattice is a partial order on T A n , the triangulations of an (n + 3)-gon. We define a partial order on T B n , the set of centrally symmetric triangulations of a (2n + 2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the An Tamari lattice, and therefore that it deserves to be… (More)

- Hugh Thomas
- Order
- 2002

A prismatoid is a polytope with all its vertices contained in two parallel facets, called its bases. Its width is the number of steps needed to go from one base to the other in the dual graph. The first author recently showed that the existence of counterexamples to the Hirsch conjecture is equivalent to that of d-prismatoids of width larger than d, and… (More)

- Hugh Thomas, Zhiqiang Wang
- 2003

This paper hypothesizes that the special role of banks as corporate quasi-insiders has been changing due to developments in informational, legal and institutional infrastructures of syn-dicated loan markets. We investigate the integration of intermediated and disintermediated financial markets through highly leveraged transaction (HLT) syndicated loans… (More)

We propose a definition of an oriented interval greedoid that simultaneously generalizes the notion of an oriented matroid and the construction on antimatroids introduced by L. of oriented matroids, associated to each oriented interval greedoid is a spherical simplicial complex whose face enumeration depends only on the underlying interval greedoid.

- Hugh Thomas
- Order
- 2006

In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice… (More)

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