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  2. Symmetric function - Wikipedia

    en.wikipedia.org/wiki/Symmetric_function

    Given any function in variables with values in an abelian group, a symmetric function can be constructed by summing values of over all permutations of the arguments. . Similarly, an anti-symmetric function can be constructed by summing over even permutations and subtracting the sum over odd permut

  3. Ring of symmetric functions - Wikipedia

    en.wikipedia.org/wiki/Ring_of_symmetric_functions

    The name "symmetric function" for elements of Λ R is a misnomer: in neither construction are the elements functions, and in fact, unlike symmetric polynomials, no function of independent variables can be associated to such elements (for instance e 1 would be the sum of all infinitely many variables, which is not defined unless restrictions are ...

  4. Symmetric probability distribution - Wikipedia

    en.wikipedia.org/wiki/Symmetric_probability...

    In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some ...

  5. Even and odd functions - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_functions

    A complex valued function is conjugate symmetric if and only if its real part is an even function and its imaginary part is an odd function. A typical example of a conjugate symmetric function is the cis function = ⁡ + ⁡ Conjugate antisymmetry:

  6. Symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Symmetric_polynomial

    One context in which symmetric polynomial functions occur is in the study of monic univariate polynomials of degree n having n roots in a given field.These n roots determine the polynomial, and when they are considered as independent variables, the coefficients of the polynomial are symmetric polynomial functions of the roots.

  7. Elementary symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Elementary_symmetric...

    That is, any symmetric polynomial P is given by an expression involving only additions and multiplication of constants and elementary symmetric polynomials. There is one elementary symmetric polynomial of degree d in n variables for each positive integer d ≤ n, and it is formed by adding together all distinct products of d distinct variables.

  8. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.

  9. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The Dirac comb of period 2 π, although not strictly a function, is a limiting form of many directional distributions. It is essentially a wrapped Dirac delta function. It represents a discrete probability distribution concentrated at 2 π n — a degenerate distribution — but the notation treats it as if it were a continuous distribution.