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2. Stars and bars (combinatorics) - Wikipedia

   en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

   For any pair of positive integers n and k, the number of k-tuples of non-negative integers whose sum is n is equal to the number of multisets of size k − 1 taken from a set of size n + 1, or equivalently, the number of multisets of size n taken from a set of size k, and is given by

3. Combinatorial optimization - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_optimization

   A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.

4. Combinatorial modelling - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_modelling

   Combinatorial modelling is the process which lets us identify a suitable mathematical model to reformulate a problem. These combinatorial models will provide, through the combinatorics theory, the operations needed to solve the problem.

5. Combinatorial explosion - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_explosion

   Then 1! = 1, 2! = 2, 3! = 6, and 4! = 24. However, we quickly get to extremely large numbers, even for relatively small n . For example, 100! ≈ 9.332 621 54 × 10 157 , a number so large that it cannot be displayed on most calculators, and vastly larger than the estimated number of fundamental particles in the observable universe.

6. Combinatorics - Wikipedia

   en.wikipedia.org/wiki/Combinatorics

   Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.

7. Combinatorial search - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_search

   Classic combinatorial search problems include solving the eight queens puzzle or evaluating moves in games with a large game tree, such as reversi or chess. A study of computational complexity theory helps to motivate combinatorial search. Combinatorial search algorithms are typically concerned with problems that are NP-hard. Such problems are ...