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  2. Orthogonal array - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_Array

    The example at left is that of an orthogonal array with symbol set {1,2} and strength 2. Notice that the four ordered pairs (2-tuples) formed by the rows restricted to the first and third columns, namely (1,1), (2,1), (1,2) and (2,2), are all the possible ordered pairs of the two element set and each appears exactly once.

  3. Mutually orthogonal Latin squares - Wikipedia

    en.wikipedia.org/wiki/Mutually_orthogonal_Latin...

    A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order n over two sets S and T (which may be the same), each consisting of n symbols, is an n × n arrangement of cells, each cell containing an ordered pair (s, t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells ...

  4. Factorial experiment - Wikipedia

    en.wikipedia.org/wiki/Factorial_experiment

    In the aquaculture experiment, the ordered triple (25, 80, 10) represents the treatment combination having the lowest level of each factor. In a general 2×3 experiment the ordered pair (2, 1) would indicate the cell in which factor A is at level 2 and factor B at level 1. The parentheses are often dropped, as shown in the accompanying table.

  5. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    McCullough and Wade [18] extended this approach, which produces all Pythagorean triples when k > h √ 2 /d: Write a positive integer h as pq 2 with p square-free and q positive. Set d = 2pq if p is odd, or d= pq if p is even. For all pairs (h,k) of positive integers, the triples are given by

  6. Sudoku solving algorithms - Wikipedia

    en.wikipedia.org/wiki/Sudoku_solving_algorithms

    A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box.

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  8. Sparse matrix - Wikipedia

    en.wikipedia.org/wiki/Sparse_matrix

    A sparse matrix obtained when solving a finite element problem in two dimensions. The non-zero elements are shown in black. The non-zero elements are shown in black. In numerical analysis and scientific computing , a sparse matrix or sparse array is a matrix in which most of the elements are zero. [ 1 ]

  9. Heap's algorithm - Wikipedia

    en.wikipedia.org/wiki/Heap's_algorithm

    The algorithm minimizes movement: it generates each permutation from the previous one by interchanging a single pair of elements; the other n−2 elements are not disturbed. In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer.