Search results
Results from the WOW.Com Content Network
Moreover it can be laborious to find m and n such that = while using it is enough to find all the () to obtain all Pythagorean triples. In particular if we need to find all primitive Pythagorean triples that involve a predetermined positive integer x now we can use only the d ∈ C ( x ) {\displaystyle d\in C(x)} that satisfy the conditions ( 2 ).
Stars and bars (combinatorics) In the context of combinatorial mathematics, stars and bars (also called "sticks and stones", [ 1 ] "balls and bars", [ 2 ] and "dots and dividers" [ 3 ]) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve many simple counting problems, such as how many ways there are to put n ...
Combination. In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple ...
and the binomial coefficient is the coefficient of the x2 term. Arranging the numbers in successive rows for n = 0, 1, 2, ... gives a triangular array called Pascal's triangle, satisfying the recurrence relation. The binomial coefficients occur in many areas of mathematics, and especially in combinatorics. In combinatorics the symbol is usually ...
Decision table. Decision tables are a concise visual representation for specifying which actions to perform depending on given conditions. Decision table is the term used for a Control table or State-transition table in the field of Business process modeling; they are usually formatted as the transpose of the way they are formatted in Software ...
The change-making problem addresses the question of finding the minimum number of coins (of certain denominations) that add up to a given amount of money. It is a special case of the integer knapsack problem, and has applications wider than just currency. It is also the most common variation of the coin change problem, a general case of ...
A truth table is a structured representation that presents all possible combinations of truth values for the input variables of a Boolean function and their corresponding output values. A function f from A to F is a special relation , a subset of A×F, which simply means that f can be listed as a list of input-output pairs.
The following algorithm generates the next permutation lexicographically after a given permutation. It changes the given permutation in-place. Find the largest index k such that a[k] < a[k + 1]. If no such index exists, the permutation is the last permutation. Find the largest index l greater than k such that a[k] < a[l].