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Abstract
A theorem due to Fröberg states that a simple graph is chordal if and only if the edge ideal of its complementary graph has a linear resolution. Actually, this is a characterization of the edge ideals of 2-uniform hypergraphs which have a linear resolution. In this article, edge ideals of a special kind of d-uniform hypergraphs is investigated. It is shown that if a d-uniform hypergraph is chordal then the edge ideal of its complementary hypergraph is weakly polymatroidal. This is an improvement of a theorem due to Emtander, Mohammadi and Moradi. Also, it is proved that all powers of the edge ideal of a Ferrers hypergraph are weakly polymatroidal.
Finally, we show that the edge ideals of a complete admissible uniform hypergraph ℋ and are weakly polymatroidal, where
is an uniform hypergraph with the edges e
c
for all edges e of ℋ.
Key Words:
2010 Mathematics Subject Classification:
ACKNOWLEDGMENT
The authors would like to thank Hassan Haghighi from K. N. Toosi University of Technology for careful reading of the article and many valuable suggestions. The authors are very grateful to the referee for several suggestions and comments that improved the article. This article finalized during Yassemi's visit of the IHES. He would like to thank the authorities of IHES for their hospitality during his stay there.
The research of S. Yassemi was in part supported by a grant from IPM No. 92130214.
Notes
Communicated by I. Swanson.