Beifang Chen

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Simple-homotopy for simplicial and CW complexes is a special kind of topological homotopy constructed by elementary collapses and expansions. In this paper we introduce graph homotopy for graphs and Graham homotopy for hypergraphs, and study the relation between these homotopies and the simplehomotopy for simplicial complexes. The graph homotopy is useful(More)
The Euler characteristic plays an important role in many subjects of discrete and continuous mathematics. For noncompact spaces, its homological definition, being a homotopy invariant, seems not as important as its role for compact spaces. However, its combinatorial definition, as a finitely additive measure, proves to be more applicable in the study of(More)
This is a survey on our work generalizing the classical Dehn-Sommerville equations (analogous to Poincaré duality, see [10]) for f -vectors of triangulations of manifolds without boundary to general polyhedra. Our key observation is that the exact data needed for the generalization is the classification of points of polyhedra by the Euler characteristics of(More)
This paper is to introduce circuit, bond, flow, and tension spaces and lattices for signed graphs, and to study the relations among these spaces and lattices. The key ingredient is to introduce circuit and bond characteristic vectors so that the desired spaces and lattices can be defined such that their dimensions and ranks match well to that of matroids of(More)
Let σ be a simplex of RN with vertices in the integral lattice ZN . The number of lattice points of mσ (= {mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0. In this paper we present: (i) a formula for the coefficients of the polynomial L(σ, t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating(More)