In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g...

of permutations occurred around 1770, when Joseph Louis Lagrange, in the study of polynomial equations, observed that properties of the permutations of...

Newton polynomial Orthogonal polynomials Orthogonal polynomials on the unit circle Permutation polynomial Racah polynomials Rogers polynomials Rogers–Szegő...

symmetric polynomial if for any permutation σ of the subscripts 1, 2, ..., n one has P(Xσ(1), Xσ(2), ..., Xσ(n)) = P(X1, X2, ..., Xn). Symmetric polynomials arise...

Permutation graph Permutation pattern Permutation polynomial Permutohedron Rencontres numbers Robinson–Schensted correspondence Sum of permutations:...

the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If...

of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group...

chess, the impetus for studying rook polynomials is their connection with counting permutations (or partial permutations) with restricted positions. A board...

in polynomial time for permutation graphs by using a longest decreasing subsequence algorithm. likewise, an increasing subsequence in a permutation corresponds...

Chebyshev polynomials. One of the main reasons for interest in them is that for fixed α, they give many examples of permutation polynomials; polynomials acting...

entries 0.: 26  An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM...

X_{i}} by an odd permutation changes the sign, while permuting them by an even permutation does not change the value of the polynomial – in fact, it is...

within a distance of S in the output). a contention-free quadratic permutation polynomial (QPP). An example of use is in the 3GPP Long Term Evolution mobile...

extension. The study of field extensions and their relationship to the polynomials that give rise to them via Galois groups is called Galois theory, so...

cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with...

orders. It is possible to test in polynomial time whether a given separable permutation is a pattern in a larger permutation, or to find the longest common...

}} of all permutations of N {\displaystyle \mathbb {N} } fixing all but a finite number of elements. They form a basis for the polynomial ring Z [ x...

solve the quintics. His argument involves studying the permutation of the roots of polynomial equations. Nevertheless, Lagrange still believed that closed-form...

of permutations of the numbers 1 to n {\textstyle n} in which exactly k {\textstyle k} elements are greater than the previous element (permutations with...

in Wiktionary, the free dictionary. QPP may refer to: Quadratic permutation polynomial Quebec Pension Plan (QPP) Queensland People's Party Queerplatonic...

automorphisms of the symmetric group Sn on the polynomial ring in n indeterminates, where a permutation acts on a polynomial by simultaneously substituting each...

corresponding permutation (which is + 1 {\displaystyle +1} for an even number of permutations and is − 1 {\displaystyle -1} for an odd number of permutations). Once...

there are n ! {\displaystyle n!} ( n {\displaystyle n} factorial) such permutation operations, the order (number of elements) of the symmetric group S n...

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable...

A one-way permutation is a one-way function that is also a permutation—that is, a one-way function that is bijective. One-way permutations are an important...

the cycles of some permutation of the Galois group of P. Another example: P being as above, a resolvent R for a group G is a polynomial whose coefficients...

weaknesses. They tried many approaches, including "knapsack-based" and "permutation polynomials". For a time, they thought what they wanted to achieve was impossible...

elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...

cycle index is a polynomial in several variables which is structured in such a way that information about how a group of permutations acts on a set can...

mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G...