Geometry of the Semigroup Z_(?0)^n and its Applications to Combinatorics, Algebra and Differential Equations

I Geometry and combinatorics of semigroups.- 1 Elementary geometry of the semigroup Zn>0.- 2 Properties of an ordered semigroup.- 3 Hilbert functions and their analogues.- II Applications: 4 Kouchnirenko`s theorem on number of solutions of a polynomial system of equations. On the Grothendieck groups of the semigroup of finite subsets of Zn and compact subsets of Rn.- 5 Differential Grobner bases and analytical theory of partial differential equations.- 6 On the Convergence of Formal Solutions of a System of Partial Differential Equations.- A Hilbert and Hilbert-Samuel polynomials and Partial Differential Equations.- References

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• Álgebra
• Teoria combinatória e dos grafos
• Geometria

Hilbert functions;Macaulay's theorem;convergence of formal solutions;ordered semigroups;solutions of partial differential equations systems