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- Combinatorial_commutative_algebra abstract "Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems arising in the other. Less obviously, polyhedral geometry plays a significant role.One of the milestones in the development of the subject was Richard Stanley's 1975 proof of the Upper Bound Conjecture for simplicial spheres, which was based on earlier work of Melvin Hochster and Gerald Reisner. While the problem can be formulated purely in geometric terms, the methods of the proof drew on commutative algebra techniques.A signature theorem in combinatorial commutative algebra is the characterization of h-vectors of simplicial polytopes conjectured in 1970 by Peter McMullen. Known as the g-theorem, it was proved in 1979 by Stanley (necessity of the conditions, algebraic argument) and by Lou Billera and Carl W. Lee (sufficiency, combinatorial and geometric construction). A major open question is the extension of this characterization from simplicial polytopes to simplicial spheres, the g-conjecture.".
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- Combinatorial_commutative_algebra wikiPageOutDegree "33".
- Combinatorial_commutative_algebra wikiPageRevisionID "674579028".
- Combinatorial_commutative_algebra wikiPageWikiLink Affine_algebraic_variety.
- Combinatorial_commutative_algebra wikiPageWikiLink Affine_variety.
- Combinatorial_commutative_algebra wikiPageWikiLink Algebraic_combinatorics.
- Combinatorial_commutative_algebra wikiPageWikiLink Bernd_Sturmfels.
- Combinatorial_commutative_algebra wikiPageWikiLink Category:Algebraic_combinatorics.
- Combinatorial_commutative_algebra wikiPageWikiLink Category:Algebraic_geometry.
- Combinatorial_commutative_algebra wikiPageWikiLink Category:Commutative_algebra.
- Combinatorial_commutative_algebra wikiPageWikiLink Claudio_Procesi.
- Combinatorial_commutative_algebra wikiPageWikiLink Cohen–Macaulay_ring.
- Combinatorial_commutative_algebra wikiPageWikiLink Combinatorics.
- Combinatorial_commutative_algebra wikiPageWikiLink Commutative_algebra.
- Combinatorial_commutative_algebra wikiPageWikiLink Convex_polytope.
- Combinatorial_commutative_algebra wikiPageWikiLink Coordinate_ring.
- Combinatorial_commutative_algebra wikiPageWikiLink Corrado_de_Concini.
- Combinatorial_commutative_algebra wikiPageWikiLink David_Eisenbud.
- Combinatorial_commutative_algebra wikiPageWikiLink G-conjecture.
- Combinatorial_commutative_algebra wikiPageWikiLink G-theorem.
- Combinatorial_commutative_algebra wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Combinatorial_commutative_algebra wikiPageWikiLink H-vector.
- Combinatorial_commutative_algebra wikiPageWikiLink Mathematics.
- Combinatorial_commutative_algebra wikiPageWikiLink Melvin_Hochster.
- Combinatorial_commutative_algebra wikiPageWikiLink Monomial_ideal.
- Combinatorial_commutative_algebra wikiPageWikiLink Monomial_ring.
- Combinatorial_commutative_algebra wikiPageWikiLink Polyhedral_combinatorics.
- Combinatorial_commutative_algebra wikiPageWikiLink Polynomial_ring.
- Combinatorial_commutative_algebra wikiPageWikiLink Richard_P._Stanley.
- Combinatorial_commutative_algebra wikiPageWikiLink Simplicial_complex.
- Combinatorial_commutative_algebra wikiPageWikiLink Simplicial_polytope.
- Combinatorial_commutative_algebra wikiPageWikiLink Simplicial_sphere.
- Combinatorial_commutative_algebra wikiPageWikiLink Stanley–Reisner_ring.
- Combinatorial_commutative_algebra wikiPageWikiLink Toric_variety.
- Combinatorial_commutative_algebra wikiPageWikiLink Upper_Bound_Conjecture.
- Combinatorial_commutative_algebra wikiPageWikiLink Upper_bound_theorem.
- Combinatorial_commutative_algebra wikiPageWikiLinkText "Combinatorial commutative algebra".
- Combinatorial_commutative_algebra wikiPageWikiLinkText "combinatorial commutative algebra".
- Combinatorial_commutative_algebra hasPhotoCollection Combinatorial_commutative_algebra.
- Combinatorial_commutative_algebra subject Category:Algebraic_combinatorics.
- Combinatorial_commutative_algebra subject Category:Algebraic_geometry.
- Combinatorial_commutative_algebra subject Category:Commutative_algebra.
- Combinatorial_commutative_algebra type Combinatoric.
- Combinatorial_commutative_algebra comment "Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems arising in the other.".
- Combinatorial_commutative_algebra label "Combinatorial commutative algebra".
- Combinatorial_commutative_algebra sameAs m.02rg1gt.
- Combinatorial_commutative_algebra sameAs Q5150822.
- Combinatorial_commutative_algebra sameAs Q5150822.
- Combinatorial_commutative_algebra wasDerivedFrom Combinatorial_commutative_algebra?oldid=674579028.
- Combinatorial_commutative_algebra isPrimaryTopicOf Combinatorial_commutative_algebra.