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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 positive integers whose sum is n is equal to the number of (k − 1)-element subsets of a set with n − 1 elements. For example, if n = 10 and k = 4, the theorem gives the number of solutions to x 1 + x 2 + x 3 + x 4 = 10 (with x 1, x 2, x 3, x 4 > 0) as the binomial coefficient

  3. Plotting algorithms for the Mandelbrot set - Wikipedia

    en.wikipedia.org/wiki/Plotting_algorithms_for...

    The first step of the second pass is to create an array of size n, which is the maximum iteration count: NumIterationsPerPixel. Next, one must iterate over the array of pixel-iteration count pairs, IterationCounts[][], and retrieve each pixel's saved iteration count, i, via e.g. i = IterationCounts[x][y].

  4. Pairwise summation - Wikipedia

    en.wikipedia.org/wiki/Pairwise_summation

    Pairwise summation is the default summation algorithm in NumPy [9] and the Julia technical-computing language, [10] where in both cases it was found to have comparable speed to naive summation (thanks to the use of a large base case).

  5. Closest pair of points problem - Wikipedia

    en.wikipedia.org/wiki/Closest_pair_of_points_problem

    The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...

  6. Non-numerical words for quantities - Wikipedia

    en.wikipedia.org/wiki/Non-numerical_words_for...

    Presumably from the practice, in counting sheep or large herds of cattle, of counting orally from one to twenty, and making a score or notch on a stick, before proceeding to count the next twenty. [3] [4] A distance of twenty yards in ancient archery and gunnery. [5] Threescore: 60 Three score (3x20) Large: 1,000 Slang for one thousand Myriad ...

  7. Enumerative combinatorics - Wikipedia

    en.wikipedia.org/wiki/Enumerative_combinatorics

    Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets S i indexed by the natural numbers , enumerative combinatorics seeks to describe a counting function which counts the number of objects in S n for each n .

  8. Subset sum problem - Wikipedia

    en.wikipedia.org/wiki/Subset_sum_problem

    The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-complete.

  9. Gauss circle problem - Wikipedia

    en.wikipedia.org/wiki/Gauss_circle_problem

    If the answer for a given is denoted by () then the following list shows the first few values of () for an integer between 0 and 12 followed by the list of values rounded to the nearest integer: 1, 5, 13, 29, 49, 81, 113, 149, 197, 253, 317, 377, 441 (sequence A000328 in the OEIS )

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