Rees algebras, Monomial Subrings and Linear Optimization Problems
msra(2010)
Abstract
In this thesis we are interested in studying algebraic properties of monomial
algebras, that can be linked to combinatorial structures, such as graphs and
clutters, and to optimization problems. A goal here is to establish bridges
between commutative algebra, combinatorics and optimization. We study the
normality and the Gorenstein property-as well as the canonical module and the
a-invariant-of Rees algebras and subrings arising from linear optimization
problems. In particular, we study algebraic properties of edge ideals and
algebras associated to uniform clutters with the max-flow min-cut property or
the packing property. We also study algebraic properties of symbolic Rees
algebras of edge ideals of graphs, edge ideals of clique clutters of
comparability graphs, and Stanley-Reisner rings.
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Key words
algebraic combinatorics,linear optimization,optimization problem
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