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RIEMANNROCH THEORY ON FINITE SETS
"... Abstract. In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a RiemannRoch Theorem for these objects (conceived as integervalued functions on the vertices). In [2] and [3] the authors generalized these concepts to realvalued functions, and proved ..."
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Abstract. In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a RiemannRoch Theorem for these objects (conceived as integervalued functions on the vertices). In [2] and [3] the authors generalized these concepts to realvalued functions, and proved a corresponding RiemannRoch Theorem in that setting, showing that it implied the BakerNorine result. In this article we prove a RiemannRoch Theorem in a more general combinatorial setting that is not necessarily driven by the existence of a graph. 1.
LINEAR SYSTEMS ON EDGEWEIGHTED GRAPHS
"... Abstract. Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are Rvalued functions on the set of vertices and graph edges are permitted to have nonnegative weights in R. Using this generalization, we provide an independent proof of a RiemannRo ..."
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Abstract. Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are Rvalued functions on the set of vertices and graph edges are permitted to have nonnegative weights in R. Using this generalization, we provide an independent proof of a RiemannRoch formula, which implies the RiemannRoch formula of Baker and Norine. 1.