A generalization of Eagon-Reiner's theorem and a characterization of bi-CMt bipartite and chordal graphs

摘要

We give a generalization of Eagon-Reiner's theorem relating Betti numbers of the Stanley-Reisner ideal of a simplicial complex and the CMt property of its Alexander dual. Then we characterize bi-CMt bipartite graphs and bi-CMt chordal graphs. These are generalizations of recent results due to Herzog and Rahimi.