Theory and Applications of Lattice Point Methods for Binomial Ideals

  • Ezra Miller
Part of the Abel Symposia book series (ABEL, volume 6)


This survey of methods surrounding lattice point methods for binomial ideals begins with a leisurely treatment of the geometric combinatorics of binomial primary decomposition. It then proceeds to three independent applications whose motivations come from outside of commutative algebra: hypergeometric systems, combinatorial game theory, and chemical dynamics. The exposition is aimed at students and researchers in algebra; it includes many examples, open problems, and elementary introductions to the motivations and background from outside of algebra.


binomial ideal primary decomposition polynomial ring affine semigroup commutative monoid lattice point convex polyhedron monomial ideal combinatorial game lattice game rational strategy misère quotient Horn hypergeometric system mass-action kinetics 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentDuke UniversityDurhamUSA

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