Sergei L. Bezrukov, Uwe Leck
The Theory of Macaulay Posets
Preprint series: Preprints aus dem Fachbereich Mathematik, Universitt Rostock
06A06 Partial order, general
05D05 Extremal set theory
Abstract: Macaulay posets are posets for which there is an analogue
of the classical Kruskal-Katona theorem for finite sets.
These posets are of great importance in many branches of
combinatorics but have numerous applications.
We survey mostly new and also some old results on Macaulay posets,
where the intension is to present them as pieces of a general theory.
In particular, the classical examples of Macaulay posets are
included as well as new ones. Emphasis is also put on construction
of Macaulay posets, and their relations to other disrete
optimization problems.
Keywords: partially ordered sets, Macaulay posets, Kruskal-Katona theorem