Search results
Results from the WOW.Com Content Network
In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer. [2] The sequence of permutations of n objects generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects.
Both the width of the rows and the permutation of the columns are usually defined by a keyword. For example, the keyword ZEBRAS is of length 6 (so the rows are of length 6), and the permutation is defined by the alphabetical order of the letters in the keyword. In this case, the order would be "6 3 2 4 1 5".
In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations can simply be made up of every permutation concatenated together, superpermutations can also be shorter (except for the trivial case of n = 1) because overlap is allowed.
Suppose the initial iteration swapped the final element with the one at (non-final) position k, and that the subsequent permutation of first n − 1 elements then moved it to position l; we compare the permutation π of all n elements with that remaining permutation σ of the first n − 1 elements.
A P-box is a permutation of all the bits: it takes the outputs of all the S-boxes of one round, permutes the bits, and feeds them into the S-boxes of the next round. A good P-box has the property that the output bits of any S-box are distributed to as many S-box inputs as possible.
The string spelled by the edges from the root to such a node is a longest repeated substring. The problem of finding the longest substring with at least k {\displaystyle k} occurrences can be solved by first preprocessing the tree to count the number of leaf descendants for each internal node, and then finding the deepest node with at least k ...
In the mathematical and computer science field of cryptography, a group of three numbers (x,y,z) is said to be a claw of two permutations f 0 and f 1 if f 0 (x) = f 1 (y) = z. A pair of permutations f 0 and f 1 are said to be claw-free if there is no efficient algorithm for computing a claw.
The study of permutation patterns began in earnest with Donald Knuth's consideration of stack-sorting in 1968. [3] Knuth showed that the permutation π can be sorted by a stack if and only if π avoids 231, and that the stack-sortable permutations are enumerated by the Catalan numbers. [4] Knuth also raised questions about sorting with deques.