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In mathematics, the coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations. [1] For example, the largest amount that cannot be obtained ...
In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form with and . in the vicinity of the regular singular point . One can divide by to obtain a differential equation of the form which will not be solvable ...
Postage stamp problem. The postage stamp problem (also called the Frobenius Coin Problem and the Chicken McNugget Theorem [1]) is a mathematical riddle that asks what is the smallest postage value which cannot be placed on an envelope, if the latter can hold only a limited number of stamps, and these may only have certain specified face values.
In group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of H, the induced representation is, in a sense, the "most general" representation of G that extends the given one. Since it is often easier to find representations of the ...
A linear recursive sequence defined by for has the characteristic polynomial , whose transpose companion matrix generates the sequence: The vector is an eigenvector of this matrix, where the eigenvalue is a root of . Setting the initial values of the sequence equal to this vector produces a geometric sequence which satisfies the recurrence.
Frobenius inner product. In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar. It is often denoted . The operation is a component-wise inner product of two matrices as though they are vectors, and satisfies the axioms for an inner product. The two matrices must have the same dimension ...
Frobenius formula. In mathematics, specifically in representation theory, the Frobenius formula, introduced by G. Frobenius, computes the characters of irreducible representations of the symmetric group Sn. Among the other applications, the formula can be used to derive the hook length formula.
Burnside's lemma can compute the number of rotationally distinct colourings of the faces of a cube using three colours.. Let X be the set of 3 6 possible face color combinations that can be applied to a fixed cube, and let the rotation group G of the cube act on X by moving the colored faces: two colorings in X belong to the same orbit precisely when one is a rotation of the other.