Abstracts
for the Seminar
Discrete Geometry and
Combinatorics
Spring 2012
Speaker: K. Chong
Title: A generalization of the colored Kruskal-Katona theorem
Time: 2:30 PM,
Monday, January 30, 2012
Place: Malott 206
Abstract:
The colored Kruskal-Katona theorem extends the Kruskal-Katona theorem and is equivalent to a numerical characterization of the f-vectors of colored complexes. The underlying theme is the study of initial sets of the reverse lexicographical order, which also plays an important role in Macaulay posets and in the computation of Hilbert functions of homogeneous ideals of certain classes of rings.
In this talk, I will give a generalization of the colored Kruskal-Katona theorem and discuss its consequences on the f-vectors of colored complexes and balanced complexes of arbitrary type. I will also give a brief introduction to Macaulay posets and Macaulay-Lex rings, and I will talk about how the generalization can yield a new class of Macaulay posets, as well as determine the Hilbert functions of homogeneous ideals of a particular class of rings.