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This is the first one of a series of papers on association of orientations, lattice polytopes, and group arrangements to graphs. The purpose is to interpret the integral and modular tension polynomials of graphs at zero and negative integers. The whole exposition is put under the framework of subgroup arrangements and the application of Ehrhart polynomials.(More)
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)