Beifang Chen

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Simple-homotopy for simplicial and CW complexes is a special kind of topo-logical 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 simple-homotopy for simplicial complexes. The graph homotopy is useful(More)
Let σ be a simplex of R N with vertices in the integral lattice Z N. 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)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Euler-ian equivalence relation on orientations, flow arrangements, and flow poly-topes; and we apply(More)
The generating function F (P) = α∈P ∩Z N x α for a rational polytope P carries all essential information of P. In this paper we show that for any positive integer n, the generating function F (P, n) of nP = {nx : x ∈ P } can be written as F (P, n) = α∈A P α (n)x nα , where A is the set of all vertices of P and each P α (n) is a certain periodic function of(More)