Concept
Permutation
Concepts associés (54)
Q-analogue
En mathématiques, plus précisément dans le domaine de la combinatoire, un q-analogue d'un théorème, d'une identité ou d'une expression est une généralisation impliquant un nouveau paramètre q et qui se spécialise en le théorème originel lorsque l'on prend la limite quand q tend vers 1. Typiquement, les mathématiciens sont intéressés par les cas où un q-analogue intervient naturellement, plutôt que par les cas où on ajoute arbitrairement un paramètre q à un théorème déjà connu.
Enumeration
An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem. Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ...
Permutohedron
In mathematics, the permutohedron of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space. Its vertex coordinates (labels) are the permutations of the first n natural numbers. The edges identify the shortest possible paths (sets of transpositions) that connect two vertices (permutations). Two permutations connected by an edge differ in only two places (one transposition), and the numbers on these places are neighbors (differ in value by 1).
Double factorial
In mathematics, the double factorial of a number n, denoted by n!!, is the product of all the positive integers up to n that have the same parity (odd or even) as n. That is, Restated, this says that for even n, the double factorial is while for odd n it is For example, 9!! = 9 × 7 × 5 × 3 × 1 = 945. The zero double factorial 0!! = 1 as an empty product. The sequence of double factorials for even n = 0, 2, 4, 6, 8,... starts as The sequence of double factorials for odd n = 1, 3, 5, 7, 9,...