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  2. Inversion (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inversion_(discrete...

    An inversion may be denoted by the pair of places (2, 4) or the pair of elements (5, 2). The inversions of this permutation using element-based notation are: (3, 1), (3, 2), (5, 1), (5, 2), and (5,4). In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order.

  3. Inversive geometry - Wikipedia

    en.wikipedia.org/wiki/Inversive_geometry

    This is called circle inversion or plane inversion. The inversion taking any point P (other than O ) to its image P ' also takes P ' back to P , so the result of applying the same inversion twice is the identity transformation which makes it a self-inversion (i.e. an involution).

  4. Reciprocal polynomial - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_polynomial

    Reciprocal polynomials have several connections with their original polynomials, including: deg p = deg p ∗ if is not 0.; p(x) = x n p ∗ (x −1). [2]α is a root of a polynomial p if and only if α −1 is a root of p ∗.

  5. Octahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Octahedral_symmetry

    The four hexagonal cycles have the inversion (the black knot on top) in common. The hexagons are symmetric, so e.g. 3 and 4 are in the same cycle. A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation.

  6. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    Integrating this relationship gives = ′ (()) +.This is only useful if the integral exists. In particular we need ′ to be non-zero across the range of integration. It follows that a function that has a continuous derivative has an inverse in a neighbourhood of every point where the derivative is non-zero.

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    Poker: Five Card Draw. Make the best five-card combination with an opportunity to draw, while enjoying structured betting. By Masque Publishing. Advertisement. Advertisement. all. board. card.

  8. Improper rotation - Wikipedia

    en.wikipedia.org/wiki/Improper_rotation

    The direct subgroup of S 2n is C n, order n, index 2, being the rotoreflection generator applied twice. For odd n, S 2n contains an inversion, denoted C i or S 2. S 2n is the direct product: S 2n = C n × S 2, if n is odd. For any n, if odd p is a divisor of n, then S 2n/p is a subgroup of S 2n, index p. For example S 4 is a subgroup of S 12 ...

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