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27 relations: Affine variety, Algebraic combinatorics, Bernd Sturmfels, Claudio Procesi, Cohen–Macaulay ring, Combinatorics, Commutative algebra, Convex polytope, Corrado de Concini, David Eisenbud, Graduate Texts in Mathematics, H-vector, Louis Billera, Mathematics, Melvin Hochster, Monomial ideal, Necessity and sufficiency, Peter McMullen, Polyhedral combinatorics, Polynomial ring, Richard P. Stanley, Simplicial complex, Simplicial polytope, Simplicial sphere, Stanley–Reisner ring, Toric variety, Upper bound theorem.
Affine variety
In algebraic geometry, an affine variety over an algebraically closed field k is the zero-locus in the affine ''n''-space k^n of some finite family of polynomials of n variables with coefficients in k that generate a prime ideal.
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Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
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Bernd Sturmfels
Bernd Sturmfels (born March 28, 1962 in Kassel, West Germany) is a Professor of Mathematics and Computer Science at the University of California, Berkeley and is a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 2017.
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Claudio Procesi
Claudio Procesi (March 31, 1941 in Rome) is an Italian mathematician, known for works in algebra and representation theory.
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Cohen–Macaulay ring
In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Commutative algebra
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
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Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
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Corrado de Concini
Corrado de Concini (born July 28, 1949 in Rome) is an Italian mathematician.
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David Eisenbud
David Eisenbud (born 8 April 1947 in New York City) is an American mathematician.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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H-vector
In algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different dimensions and allows one to express the Dehn–Sommerville equations in a particularly simple form.
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Louis Billera
Louis Joseph Billera is a Professor of Mathematics at Cornell University.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Melvin Hochster
Melvin Hochster (born August 2, 1943) is an eminent American mathematician, regarded as one of the leading commutative algebraists active today.
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Monomial ideal
In algebra, a monomial ideal is an ideal generated by some monomials in a multivariate polynomial ring over a field.
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Necessity and sufficiency
In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.
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Peter McMullen
Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.
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Polyhedral combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
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Polynomial ring
In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
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Richard P. Stanley
Richard Peter Stanley (born June 23, 1944 in New York City, New York) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts.
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Simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).
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Simplicial polytope
In geometry, a simplicial polytope is a polytope whose facets are all simplices.
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Simplicial sphere
In geometry and combinatorics, a simplicial (or combinatorial) d-sphere is a simplicial complex homeomorphic to the ''d''-dimensional sphere.
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Stanley–Reisner ring
In mathematics, a Stanley–Reisner ring is a quotient of a polynomial algebra over a field by a square-free monomial ideal.
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Toric variety
In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety.
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Upper bound theorem
In mathematics, the upper bound theorem states that cyclic polytopes have the largest possible number of faces among all convex polytopes with a given dimension and number of vertices.
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References
[1] https://en.wikipedia.org/wiki/Combinatorial_commutative_algebra
