Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Spring 2015

Speaker:  Ernest Chong, Cornell University
Title: Kruskal-Katona-type theorems
Time: 2:30 PM, Monday, January 26, 2015
Place:  Malott 206

Abstract: The Kruskal-Katona theorem, proven around the 1960s, is a classic result in combinatorics that characterizes the f-vectors of simplicial complexes. In 1977, Stanley noticed that Macaulay's well-known characterization of the Hilbert functions of graded ideals of polynomial rings is equivalent to a multiset analogue of the Kruskal-Katona theorem. Later in 1988, Frankl-Füredi-Kalai found a graph-theoretic analogue of the Kruskal-Katona theorem. The purpose of this talk is to reconcile these Kruskal-Katona analogues using the algebraic notion of Macaulay-Lex rings. We will show that these analogues are in fact special cases of one main theorem.

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