of permutations of n items selected r at the same. By applying the above rule in order to fill up the odd places, we. The meaning of PERMUTE is to change the order or arrangement of especially : to arrange in all possible ways. In a quite simple wordings, a permutation is a system of objects in a well-defined order. For example primitive groups other than $A_n$ and $S_n$ have bases of length $O(\sqrt \log n)$, which can be improved to $O(\log n)$ by excluding some known families of examples. Because we have already used two letters in the even places. Many groups with which we wish to compute have bases of length much less than $n$, and there are lots of results (by Babai, Shalev, Liebeck, et al) proving the existence of bases with bounded length in certain families of groups. ![]() These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age. Now, this enormous number was not found by counting them. For example, if twelve different things are permuted, then the number of their permutations is 479,001,600. Put simply, a permutation is a word that. An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. As the number of things (letters) increases, their permutations grow astronomically. ![]() This is perhaps the single most important reason why bases play such a fundamental role in computations in permutation groups. The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. As has been pointed out in comments, you cannot hope to do better in general than $O(n(l_1+l_2))$, where $n$ is the degree of the permutation groups and $l_1$, $l_2$ are the lengths of the words.īut from a practical point of view it is important to observe that once a base for $G$ has been computed (see my answer to this question), the word problem can be solved in time $O(k(l_1+l_2)$, where $k$ is the length of the base, because elements of the group are uniquely determined by their actions on the base.
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