Some New Results on Macaulay Posets

Abstract

Macaulay posets are posets for which there is an analogue of the classical KruskalKatona theorem for finite sets. These posets are of great importance in many branches of combinatorics and have numerous applications. We survey mostly new and also some old results on Macaulay posets. Emphasis is also put on construction of extremal ideals in Macaulay posets.

On minimisation of the double-sided shadow in the unit cube

“…Analogues of Kruskal-Katona's theorem have been proved also for the Cartesian product of stars [7] and the dual partially ordered set [8].…”