组合交换代数

Thelastdecadehasseenanumberofexcitingdevelopmentsattheintersectionofcommutativealgebrawithcombinatorics.Newmethodshaveevolvedoutofaninfluxofideasfromsuchdiverseareasaspolyhedralgeometry，theoreticalphysics，representationtheory，homologicalalgebra，symplecticgeometry，graphtheory，integerprogramming，symboliccomputation，andstatistics.Thepurposeofthisvolumeistoprovideaselfcontainedintroductiontosomeoftheresultingcombinatorialtechniquesfordealingwithpolynomialrings，semigrouprings，anddeterminantalrings.Ourexpositionmainlyconcernscombinatoriallydefinedidealsandtheirquotients，withafocusonnumericalinvariantsandresolutions，especiallyundergradingsmorerefinedthanthestandardintegergrading.