Inclusion Orders: New Algebraic Techniques Desperately Needed
by
William T. Trotter
Arizona State University

One of the most natural ways to generate a partial order is to consider a family of sets ordered by the inclusion relation. For example, distributive lattices are just the down sets of a poset ordered by inclusion, and in fact every poset is the inclusion order of some family of sets. On the other hand, one of the most widely studied instances of inclusion orders results from restricting the sets to be geometric objects, e.g., boxes, cubes, spheres, circles, ellipses, etc. In this talk, we report on some recent research on geometric inclusion orders - highlighting the key role played by algebraic techniques. However, we will also point out the limitations of known results and (hopefully) motivate some interest in developing new methods with a broader range of applicability to inclusion orders.

Date received: May 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafg-12.