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The aim of this book is to give a description on the algebra associating to hypergraph, which is the generalized form of simple graphs and simplicial complexes. Algebraic study of combinatorial objects has been widely studied by different algebraist. Our main work in this regard is to associate an algebra to a special class of hypergraphs namely uniformly increasing hypergraphs H(X, E, d). This class of hypergraphs is important in one sense that they can neither be treated as simple graphs nor simplicial complexes. So, this work is the first stepping towards exploring the algebra associated...

The aim of this book is to explore the algebraic and combinatorial properties of simplicial complexes. Let S = k[x1, x2, ..., xn] be a polynomial ring over an infinite field k. Note that, there is a natural bijection between the square-free monomial ideals (so called non facet ideals) and simplicial complexes introduced by R.P. Stanley. Later Faridi introduced another correspondence betweeen the square-free monomial ideals (so called facet ideals) and simplicial complexes. So, corresponding to a square-free monomial ideal I in S, one can consider I as the facet ideal of one simplicial complex...