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8 relations: Bernstein–Kushnirenko theorem, Combinatorial mirror symmetry, Discrete geometry, Integer points in convex polyhedra, Linear programming, Normal polytope, Polyhedron, Z-polyhedron.
Bernstein–Kushnirenko theorem
Bernstein–Kushnirenko theorem (also known as BKK theorem or Bernstein–Khovanskii–Kushnirenko theorem), proven by David Bernstein and in 1975, is a theorem in algebra.
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Combinatorial mirror symmetry
A purely combinatorial approach to mirror symmetry was suggested by Victor Batyrev using the polar duality for d-dimensional convex polyhedra.
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Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
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Integer points in convex polyhedra
The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative integer-valued solutions does a system of linear equations with nonnegative coefficients have" or "how many solutions does an integer linear program have".
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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Normal polytope
In mathematics, specifically in combinatorial commutative algebra, a convex lattice polytope P is called normal if it has the following property: given any positive integer n, every lattice point of the dilation nP, obtained from P by scaling its vertices by the factor n and taking the convex hull of the resulting points, can be written as the sum of exactly n lattice points in P. This property plays an important role in the theory of toric varieties, where it corresponds to projective normality of the toric variety determined by P. Normal polytopes have popularity in algebraic combinatorics.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Z-polyhedron
Z-polyhedron or Z-polytope may refer to.
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