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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.".
- Combinatorial_commutative_algebra wikiPageID "11503412".
- Combinatorial_commutative_algebra wikiPageRevisionID "565678566".
- 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 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=565678566.
- Combinatorial_commutative_algebra isPrimaryTopicOf Combinatorial_commutative_algebra.