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64 relations: Abstract polytope, Aequationes Mathematicae, American Mathematical Society, Annals of Mathematics, Balinski's theorem, Birkhoff polytope, Bit array, Bulletin of the American Mathematical Society, Combinatorial commutative algebra, Combinatorics, Complete bipartite graph, Complete graph, Connectivity (graph theory), Convex combination, Convex polytope, Cube, Cutting-plane method, Dehn–Sommerville equations, Diameter, Discrete & Computational Geometry, Discrete geometry, Double counting (proof technique), Dual polyhedron, Edge (geometry), Euler characteristic, Existential theory of the reals, Face (geometry), Facet (geometry), Graph (discrete mathematics), H-vector, Hirsch conjecture, Hypercube, Inequality (mathematics), Information Processing Letters, Integer programming, Journal of Combinatorial Theory, K-vertex-connected graph, Line segment, Linear inequality, Linear programming, Matching (graph theory), Mathematical Programming, Mathematics, Matroid polytope, Micha Perles, N-skeleton, Neighborly polytope, Octahedron, Partially ordered set, Permutation matrix, ..., Planar graph, PP (complexity), Simple polytope, Simplex, Simplex algorithm, Simplicial polytope, Simplicial sphere, Steinitz's theorem, Time complexity, Unimodality, Unique sink orientation, Upper and lower bounds, Upper bound theorem, Vertex (geometry). Expand index (14 more) »
Abstract polytope
In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope, but not any purely geometric properties such as angles, edge lengths, etc.
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Aequationes Mathematicae
Aequationes Mathematicae is a mathematical journal.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Annals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.
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Balinski's theorem
In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes.
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Birkhoff polytope
The Birkhoff polytope Bn, also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete bipartite graph K_, is the convex polytope in RN (where N.
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Bit array
A bit array (also known as bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits.
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Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
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Combinatorial commutative algebra
Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline.
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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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Complete bipartite graph
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Complete graph
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Connectivity (graph theory)
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to disconnect the remaining nodes from each other.
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Convex combination
In convex geometry, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.
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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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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cutting-plane method
In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts.
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Dehn–Sommerville equations
In mathematics, the Dehn–Sommerville equations are a complete set of linear relations between the numbers of faces of different dimension of a simplicial polytope.
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Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
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Discrete & Computational Geometry
Discrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer.
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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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Double counting (proof technique)
In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set.
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Dual polyhedron
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.
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Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
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Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
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Existential theory of the reals
In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form where F(X_1,\dots X_n) is a quantifier-free formula involving equalities and inequalities of real polynomials.
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Face (geometry)
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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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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Hirsch conjecture
In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n − d.
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Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
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Inequality (mathematics)
In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).
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Information Processing Letters
Information Processing Letters is a peer reviewed scientific journal in the field of computer science, published by Elsevier.
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Integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
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Journal of Combinatorial Theory
The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas.
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K-vertex-connected graph
In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.
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Line segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
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Linear inequality
In mathematics a linear inequality is an inequality which involves a linear function.
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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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Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
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Mathematical Programming
Mathematical Programming is a peer-reviewed scientific journal that was established in 1971 and is published by Springer Science+Business Media.
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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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Matroid polytope
In mathematics, a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is a polytope constructed via the bases of a matroid.
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Micha Perles
Micha Asher Perles is an Israeli mathematician working in geometry, a professor emeritus at the Hebrew University.
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N-skeleton
In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.
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Neighborly polytope
In geometry and polyhedral combinatorics, a k-neighborly polytope is a convex polytope in which every set of k or fewer vertices forms a face.
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Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Permutation matrix
\pi.
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Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
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PP (complexity)
In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances.
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Simple polytope
In geometry, a d-dimensional simple polytope is a d-dimensional polytope each of whose vertices are adjacent to exactly d edges (also d facets).
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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Simplex algorithm
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.
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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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Steinitz's theorem
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices).
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Unimodality
In mathematics, unimodality means possessing a unique mode.
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Unique sink orientation
In mathematics, a unique sink orientation is an orientation of the edges of a polytope such that, in every face of the polytope (including the whole polytope as one of the faces), there is exactly one vertex for which all adjoining edges are oriented inward (i.e. towards that vertex).
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Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (K, ≤) is an element of K which is greater than or equal to every element of S. The term lower bound is defined dually as an element of K which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
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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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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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References
[1] https://en.wikipedia.org/wiki/Polyhedral_combinatorics
