組合交換代數(shù)
Thelastdecadehasseenanumberofexcitingdevelopmentsattheintersectionofcommutativealgebrawithcombinatorics.Newmethodshaveevolvedoutofaninfluxofideasfromsuchdiverseareasaspolyhedralgeometry,theoreticalphysics,representationtheory,homologicalalgebra,symplecticgeometry,graphtheory,integerprogramming,symboliccomputation,andstatistics.Thepurposeofthisvolumeistoprovideaselfcontainedintr...
Thelastdecadehasseenanumberofexcitingdevelopmentsattheintersectionofcommutativealgebrawithcombinatorics.Newmethodshaveevolvedoutofaninfluxofideasfromsuchdiverseareasaspolyhedralgeometry,theoreticalphysics,representationtheory,homologicalalgebra,symplecticgeometry,graphtheory,integerprogramming,symboliccomputation,andstatistics.Thepurposeofthisvolumeistoprovideaselfcontainedintroductiontosomeoftheresultingcombinatorialtechniquesfordealingwithpolynomialrings,semigrouprings,anddeterminantalrings.Ourexpositionmainlyconcernscombinatoriallydefinedidealsandtheirquotients,withafocusonnumericalinvariantsandresolutions,especiallyundergradingsmorerefinedthanthestandardintegergrading.
