About: Combinatorial commutative algebra

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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.

Attributes	Values
rdfs:label	Combinatorial commutative algebra (en)
rdfs: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. Less obviously, polyhedral geometry plays a significant role. (en)
dcterms:subject	Algebraic combinatorics Commutative algebra Algebraic geometry
Wikipage page ID	11503412 (xsd:integer)
Wikipage revision ID	928372636 (xsd:integer)
Link from a Wikipage to another Wikipage	Bernd Sturmfels David Eisenbud Algebraic combinatorics Algebraic combinatorics Peter McMullen Richard P. Stanley Zero-divisor graph Corrado de Concini Mathematics Melvin Hochster Louis Billera Monomial ideal Convex polytope Simplicial sphere Claudio Procesi Combinatorics Commutative algebra G-conjecture G-theorem H-vector Graduate Texts in Mathematics Simplicial complex Commutative algebra Algebraic geometry Karim Adiprasito Cohen–Macaulay ring Toric variety Polyhedral combinatorics Polynomial ring Coordinate ring Necessity and sufficiency Simplicial polytope Stanley–Reisner ring Affine algebraic variety Upper Bound Conjecture dbr:Monomial_ring
sameAs	Combinatorial commutative algebra Combinatorial commutative algebra Combinatorial commutative algebra
dbp:wikiPageUsesTemplate	dbt:ISBN
has 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 Louis Billera and Carl W. Lee (sufficiency, combinatorial and geometric construction). A major open question was the extension of this characterization from simplicial polytopes to simplicial spheres, the g-conjecture, which was resolved in 2018 by Karim Adiprasito. (en)
prov:wasDerivedFrom	wikipedia-en:Combinatorial_commutative_algebra?oldid=928372636&ns=0
page length (characters) of wiki page	4175 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Combinatorial_commutative_algebra
is Link from a Wikipage to another Wikipage of	List of commutative algebra topics Melody Chan Algebraic combinatorics Cyclic polytope Zero-divisor graph Louis Billera Normal polytope Glossary of areas of mathematics Siamak Yassemi Commutative algebra Polyhedral combinatorics Stanley–Reisner ring
is foaf:primaryTopic of	wikipedia-en:Combinatorial_commutative_algebra

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