Synonymer & Information om | Engelska ordet COMBINATORIAL

Exempel på hur du använder COMBINATORIAL i en mening

• Quantum annealing, a method for solving combinatorial optimisation problems and ground states of glassy systems.
• Such dual figures remain combinatorial or abstract polyhedra, but not all can also be constructed as geometric polyhedra.
• He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
• In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.
• In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim, or to an infinite generalization of nim.
• Problems known to be PSPACE-complete include determining properties of regular expressions and context-sensitive grammars, determining the truth of quantified Boolean formulas, step-by-step changes between solutions of combinatorial optimization problems, and many puzzles and games.
• In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric.
• Pisanski’s research interests span several areas of discrete and computational mathematics, including combinatorial configurations, abstract polytopes, maps on surfaces, chemical graph theory, and the history of mathematics and science.
• It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert.
• It was posed by William Burnside in 1902, making it one of the oldest questions in group theory, and was influential in the development of combinatorial group theory.
• In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for deriving the generating functions of discrete structures, which allows one to not merely count these structures but give bijective proofs involving them.
• In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position.
• In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim.
• Brouwer also proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, of the treatment of general continuous mappings.
• In the particular case where the space is a finite-dimensional Euclidean space, each site is a point, there are finitely many points and all of them are different, then the Voronoi cells are convex polytopes and they can be represented in a combinatorial way using their vertices, sides, two-dimensional faces, etc.
• This initiated the combinatorial theory now called Ramsey theory, that seeks regularity amid disorder: general conditions for the existence of substructures with regular properties.
• The basic combinatorial question is, How many different polyiamonds exist with a given number of cells? Like polyominoes, polyiamonds may be either free or one-sided.
• In this way, the combinatorial formulation for finite families of finite sets and the graph-theoretic formulation for finite graphs are equivalent.
• In statistical mechanics, combinatorial numbers reach such immense magnitudes that they are often expressed using logarithms.
• Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research.

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