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Possible patterns of bracelets of length n corresponding to the k-th integer partition (set partitions up to rotation and reflection)For a given set of n beads, all distinct, the number of distinct necklaces made from these beads, counting rotated necklaces as the same, is n! / n = (n − 1)!.
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In mathematics, an idempotent binary relation is a binary relation R on a set X (a subset of Cartesian product X × X) for which the composition of relations R ∘ R is the same as R. [ 1 ] [ 2 ] This notion generalizes that of an idempotent function to relations.
In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. [1] Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation.
A binary operation is a binary function where the sets X, Y, and Z are all equal; binary operations are often used to define algebraic structures. In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f x and f y are all linear transformations.
In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation.
For complementary sequences in biology, see complementarity (molecular biology).For integer sequences with complementary sets of members see Lambek–Moser theorem.. In applied mathematics, complementary sequences (CS) are pairs of sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero.
In mathematics, the reflexive closure of a binary relation on a set is the smallest reflexive relation on that contains . A relation is called reflexive if it relates every element of to itself.