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Paper   IPM / M / 14988
School of Mathematics
  Title:   On the facet ideal of an expanded simplicial complex
1.  Somayeh Moradi
2.  Rahim Rahmati-Asghar
  Status:   To Appear
  Journal: Bull. Iranian Math. Soc.
  Supported by:  IPM
For a simplicial complex ∆�??, �??the affect of the expansion functor on combinatorial properties of ∆ and algebraic properties of its Stanley-Reisner ring has been studied in some previous papers�??. �??In this paper�??, �??we consider the facet ideal I(∆) and its Alexander dual which we denote by J to see how the expansion functor alter the algebraic properties of these ideals�??. �??It is shown that for any expansion ∆α the ideals J and Jα have the same total Betti numbers and their Cohen-Macaulayness are equivalent�??, �??which implies that the regularities of the ideals I(∆) and I(∆α) are equal�??. �??Moreover�??, �??the projective dimensions of I(∆) and I(∆α) are compared�??. �??In the sequel for a graph G�??, �??some properties that are equivalent in G and its expansions are presented and for a Cohen-Macaulay (resp�??. �??sequentially Cohen-Macaulay and shellable) graph G�??, �??we give some conditions for adding or removing a vertex from G�??, �??so that the remaining graph is still Cohen-Macaulay (resp�??. �??sequentially Cohen-Macaulay and shellable).

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