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Monomial Algebras, Second Edition presents algebraic,
combinatorial, and computational methods for studying monomial
algebras and their ideals, including Stanley-Reisner rings,
monomial subrings, Ehrhart rings, and blowup algebras. It
emphasizes square-free monomials and the corresponding graphs,
clutters, or hypergraphs. New to the Second Edition Four new
chapters that focus on the algebraic properties of blowup algebras
in combinatorial optimization problems of clutters and hypergraphs
Two new chapters that explore the algebraic and combinatorial
properties of the edge ideal of clutters and hypergraphs Full
revisions of existing chapters to provide an up-to-date account of
the subject Bringing together several areas of pure and applied
mathematics, this book shows how monomial algebras are related to
polyhedral geometry, combinatorial optimization, and combinatorics
of hypergraphs. It directly links the algebraic properties of
monomial algebras to combinatorial structures (such as simplicial
complexes, posets, digraphs, graphs, and clutters) and linear
optimization problems.
Monomial Algebras, Second Edition presents algebraic,
combinatorial, and computational methods for studying monomial
algebras and their ideals, including Stanley-Reisner rings,
monomial subrings, Ehrhart rings, and blowup algebras. It
emphasizes square-free monomials and the corresponding graphs,
clutters, or hypergraphs. New to the Second Edition Four new
chapters that focus on the algebraic properties of blowup algebras
in combinatorial optimization problems of clutters and hypergraphs
Two new chapters that explore the algebraic and combinatorial
properties of the edge ideal of clutters and hypergraphs Full
revisions of existing chapters to provide an up-to-date account of
the subject Bringing together several areas of pure and applied
mathematics, this book shows how monomial algebras are related to
polyhedral geometry, combinatorial optimization, and combinatorics
of hypergraphs. It directly links the algebraic properties of
monomial algebras to combinatorial structures (such as simplicial
complexes, posets, digraphs, graphs, and clutters) and linear
optimization problems.
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