The Whitney numbers and the product of partially ordered sets
by
Agnieszka Julia Marasik
Warsaw University of Technology
Coauthors: Aleksander Rutkowski

Let consider the Cartesian product of finite partially ordered sets. Our aim is to estimate the width of it (the maximum over numbers of elements of all antichains in this partially ordered set).

It is appear, that in the case the product of chains and some subsets of it, the width is realized by one of the Whitney numbers - the numbers of elements of the same rang. We calculate Whitney numbers of the product of three chains and some subset of it and product of four chains and as a consequence we get the width of these partially ordered sets.

Date received: July 6, 2002

Copyright © 2002 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 # caiv-47.