Let S be a finite alphabet. An injective word over S is a word over S such that each letter in S appears at most once in the word. We study Boolean cell complexes of injective words over S and their commutation classes. This generalizes work by Farmer and by Björner and Wachs on the complex of all injective words. Specifically, for an abstract simplicial complex ∆, we consider the Boolean cell ...

We call a vertex x of a graph G = (V,E) a codominated vertex if NG[y] ⊆ NG[x] for some vertex y ∈ V \{x}, and a graph G is called codismantlable if either it is an edgeless graph or it contains a codominated vertex x such that G − x is codismantlable. We show that (C4, C5)-free vertex-decomposable graphs are codismantlable, and prove that if G is a (C4, C5, C7)-free well-covered graph, then ver...

Robert Peters,1,* Shintaro Hoshino,2 Norio Kawakami,1 Junya Otsuki,2,3 and Yoshio Kuramoto2 1Department of Physics, Kyoto University, Kyoto 606-8502, Japan 2Department of Physics, Tohoku University, Sendai 980-8578, Japan 3Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany (Received 21 February 2013;...

Let S be a finite alphabet. An injective word over S is a word over S such that each letter in S appears at most once in the word. We study Boolean cell complexes of injective words over S and their commutation classes. This generalizes work by Farmer and by Björner and Wachs on the complex of all injective words. Specifically, for an abstract simplicial complex ∆, we consider the Boolean cell ...

Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring,  named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists  such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...

Given a finite simple undirected graph G there is simplicial complex Ind(G), called the independence complex, whose faces correspond to independent sets of G. This well-studied concept because it provides fertile ground for interactions between commutative algebra, theory and algebraic topology. In this paper, we consider generalization complex. [Formula: see text], subset vertex set r-independ...

In this paper, we discuss the relation between shellability, sequentially CohenMacaulayness, and partitionability. Especially, our main concern is to see the difference of these properties when we require heredity. For a property P, we say a simplicial complex satisfies hereditary-P if the simplicial complex itself and all the restrictions to subsets of its vertex set satisfy the property P, an...