Geodesic
Riemann-Roch theory on finite sets
Journal of Singularities, Tome 9 (2014), pp. 75-81

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M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In earlier works, we generalized these concepts to real-valued functions, and proved a corresponding Riemann-Roch Theorem in that setting, showing that it implied the Baker-Norine result. In this article we prove a Riemann-Roch Theorem in a more general combinatorial setting that is not necessarily driven by the existence of a graph. 
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     author = {Rodney James and Rick Miranda},
     title = {Riemann-Roch theory on finite sets},
     journal = {Journal of Singularities},
     pages = {75--81},
     publisher = {mathdoc},
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     year = {2014},
     doi = {10.5427/jsing.2014.9g},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.9g/}
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Rodney James; Rick Miranda. Riemann-Roch theory on finite sets. Journal of Singularities, Tome 9 (2014), pp. 75-81. doi: 10.5427/jsing.2014.9g

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