# Algebra & Combinatorics Seminar Thursday, Oct. 18 at 10am

*Title:* **Poset structure and dimension bounds.**

*When/Where: *10:00am Thursday, October 18^{th}, Natural Sciences Building, Room 234

*Speaker: *Professor Biro

Department of Mathematics, UofL

Abstract:

Planar partially ordered sets can have arbitrarily large dimension. There are known results for the upper bound of planar posets if we bound the height, or if we bound the number of minimal (maximal) elements. On the other hand, for posets that are not necessarily planar, but other structural properties are imposed, the dimension is bounded in terms of the height. In this talk, we survey some of these theorems, and we introduce a new result: planar posets that are accessible from below are of dimension at most 6.

The talk will introduce all definitions and background information, so prior understanding of poset theory is not required.