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The bit reversal permutation has also been used to devise lower bounds in distributed computation. [8] The Van der Corput sequence, a low-discrepancy sequence of numbers in the unit interval, is formed by reinterpreting the indexes of the bit-reversal permutation as the fixed-point binary representations of dyadic rational numbers.
Multiplying a matrix M by either or on either the left or the right will permute either the rows or columns of M by either π or π −1.The details are a bit tricky. To begin with, when we permute the entries of a vector (, …,) by some permutation π, we move the entry of the input vector into the () slot of the output vector.
An exchange matrix is the simplest anti-diagonal matrix. Any matrix A satisfying the condition AJ = JA is said to be centrosymmetric. Any matrix A satisfying the condition AJ = JA T is said to be persymmetric. Symmetric matrices A that satisfy the condition AJ = JA are called bisymmetric matrices. Bisymmetric matrices are both centrosymmetric ...
The Fredkin gate is a universal reversible 3-bit gate that swaps the last two bits if the first bit is 1; a controlled-swap operation. The n-bit Toffoli gate is a generalization of the Toffoli gate. It takes n bits x 1, x 2, ..., x n as inputs and outputs n bits. The first n − 1 output bits are just x 1, ..., x n−1. The last output bit is ...
Parity of a permutation; Permanent (mathematics) Permutable prime; Permutation (music) Permutation automaton; Permutation box; Permutation matrix; Permutation polynomial; Permutoassociahedron; Permutohedron; Place-permutation action; Plain hunt; Pseudorandom permutation
The meaning is as follows: the first bit of the output is taken from the 58th bit of the input; the second bit from the 50th bit, and so on, with the last bit of the output taken from the 7th bit of the input. This information is presented as a table for ease of presentation; it is a vector, not a matrix.
Enumerations of specific permutation classes; Factorial. Falling factorial; Permutation matrix. Generalized permutation matrix; Inversion (discrete mathematics) Major index; Ménage problem; Permutation graph; Permutation pattern; Permutation polynomial; Permutohedron; Rencontres numbers; Robinson–Schensted correspondence; Sum of permutations ...
Permuting the vertices on each level of the Stern–Brocot tree by a bit-reversal permutation produces a different tree, the Calkin–Wilf tree, in which the children of each number a / b are the two numbers a / a + b and a + b / b . Like the Stern–Brocot tree, the Calkin–Wilf tree contains each positive rational ...