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A main problem in permutation codes is to determine the value of (,), where (,) is defined to be the maximum number of codewords in a permutation code of length and minimum distance . There has been little progress made for 4 ≤ d ≤ n − 1 {\displaystyle 4\leq d\leq n-1} , except for small lengths.
Programming by permutation gives little or no assurance about the quality of the code produced—it is the polar opposite of formal verification. Programmers are often compelled to program by permutation when an API is insufficiently documented.
In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion table. The Lehmer code is named in reference to D. H. Lehmer, [1] but the code had been known since 1888 ...
A map of the 24 permutations and the 23 swaps used in Heap's algorithm permuting the four letters A (amber), B (blue), C (cyan) and D (dark red) Wheel diagram of all permutations of length = generated by Heap's algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red).
Permute instructions occur in both scalar processors as well as vector processing engines as well as GPUs.In vector instruction sets they are typically named "Register Gather/Scatter" operations such as in RISC-V vectors, [2] and take Vectors as input for both source elements and source array, and output another Vector.
More generally, combinatorial algorithms researchers have defined a Gray code for a set of combinatorial objects to be an ordering for the objects in which each two consecutive objects differ in the minimal possible way. In this generalized sense, the Steinhaus–Johnson–Trotter algorithm generates a Gray code for the permutations themselves ...
This version is dangerous because if the count is 0 or 32, it asks for a 32-bit shift, which is undefined behaviour in the C language standard. However, it tends to work anyway, because most microprocessors implement value >> 32 as either a 32-bit shift (producing 0) or a 0-bit shift (producing the original value ), and either one produces the ...
27 languages. العربية ... Download QR code; Print/export Download as PDF; ... Permutation groups (1 C, 33 P) Permutation patterns (15 P) S. Serialism (2 C, 10 ...