Kerrin Bielser: On Certain Properties of Special Macaulay Posets

Macaulay posets are posets with an additional total order satisfying a condition that generalises the Kruskal-Katona theorem.  There are some properties that are of particular interest to these posts. After an introduction to the topic, this talk will focus on a class of Macaulay posets called Leck posets. Using visualisation diagrams, we will prove that Leck posets have the property of being final shadow increasing, which implies other interesting properties of Leck posets and their duals, such as being Sperner posets. In addition, a more general condition for another shadow propery, namely additivity, will be presented.