Monomial Algebras

Preface 1 Polyhedral Geometry and Linear Optimization 2 Commutative Algebra 3 Affine and Graded Algebras 4 Rees Algebras and Normality 5 Hilbert Series and Gorenstein Rings 6 Stanley-Reisner Rings and Edge Ideals 7 Edge Ideals of Graphs 8 Toric Ideals and Affine Varieties 9 Linear and Reed-Muller Type Codes 10 Monomial Subrings 11 Monomial Subrings of Graphs 12 Edge Subrings and Combinatorial Optimization 13 Normality of Rees Algebras of Monomial Ideals 14 Combinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters 15 Combinatorial Optimization and Blowup Algebras 16 The Containment Problem and the Resurgence of Ideals A Procedures for Macaulay2 and Normaliz B Graph Diagrams Bibliography Notation Index Index

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• A matemática discreta
• Álgebra
• Teoria combinatória e dos grafos
• Teoria dos números

commutative ring theory;polyhedral combinatorics;symbolic powers;Gorenstein properties;computational algebraic geometry;coding theory applications;algebraic methods in combinatorial optimization