Georgia Institute of Technology College of Sciences

The original concept ofdimension for posets was formulatedby Dushnik and Miller in 1941 and hasbeen studied extensively in the literature.Over the years, a number of variant formsof dimension have been proposed withvarying degrees of interest and application.However, in the recent past, two variantshave received extensive attention. Theyare Boolean dimension and local dimension.This is the first of two talks on these twoconcepts, with the second talk givenby Heather Smith. In this talk, wewill introduce the two parameters and providemotivation for their study. We will alsogive some concrete examples andprove some basic inequalities.This is joint work with a GeorgiaTech team in which my colleaguesare Fidel Barrera-Cruz, Tom Prag,Heather Smith and Libby Taylor.