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          組合交換代數(shù)

          聯(lián)合創(chuàng)作 · 2023-09-28 18:13

          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.

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