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Let ∆n−1 denote the (n − 1)-dimensional simplex. Let Y be a random k-dimensional subcomplex of ∆n−1 obtained by starting with the full (k − 1)-dimensional skeleton of ∆n−1 and then adding each k-simplex independently with probability p. Let Hk−1(Y ;R) denote the (k−1)-dimensional reduced homology group of Y with coefficients in a finite abelian group R. It(More)
The flag complex of a graph G = (V,E) is the simplicial complex X(G) on the vertex set V whose simplices are subsets of V which span complete subgraphs of G. We study relations between the first eigenvalues of successive higher Laplacians of X(G). One consequence is the following Theorem: Let λ2(G) denote the second smallest eigenvalue of the Laplacian of(More)
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