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971.
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The Laplacian and Dirac operators on critical planar graphs 总被引:6,自引:0,他引:6
R. Kenyon 《Inventiones Mathematicae》2002,150(2):409-439
On a periodic planar graph whose edge weights satisfy a certain simple geometric condition, the discrete Laplacian and Dirac
operators have the property that their determinants and inverses only depend on the local geometry of the graph. We obtain
explicit expressions for the logarithms of the (normalized) determinants, as well as the inverses of these operators. We relate
the logarithm of the determinants to the volume plus mean curvature of an associated hyperbolic ideal polyhedron. In the associated
dimer and spanning tree models, for which the determinants of the Dirac operator and the Laplacian respectively play the role
of the partition function, this allows us to compute the entropy and correlations in terms of the local geometry. In addition,
we define a continuous family of special discrete holomorphic functions which, via convolutions, gives a general process for
constructing discrete holomorphic functions and discrete harmonic functions on critical planar graphs.
Oblatum 6-III-2002 & 12-VI-2002?Published online: 6 August 2002 相似文献
974.
Roger M. Hill 《The Journal of the Operational Research Society》1989,40(11):983-992
The context is that of a retail chain where stock is purchased into a central warehouse from which branch stocks are replenished. This paper considers possible methods of allocating limited warehouse stock to branches, and uses simulation to quantify the resulting benefits. 相似文献
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Let G=(V,E) be a undirected k-edge connected graph with weights ce on edges and wv on nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G, of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable. 相似文献
980.