11/24/2023 0 Comments Permutation mathwe might ask how many ways we can arrange 2 letters from that set. For example, suppose we have a set of three letters: A, B, and C. So in that sense you can argue that 'NO' is the 'better' answer. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. But other people might have other preferences. The argumentation for 'NO' relies on a hard mathematical fact (the formula works in both cases) the argument for 'YES' relies on a personal preference for quick algorithms that I already know over slower or more complicated or equally easy but yet unknown to me algorithms. Of course there is a difference between the two answers. (I can edit it in if you want, but you probably already know it). Reason: there is a very quick and easy algorithm for writing your permutation in this form. Is there any reason for writing it as a product of DISJOINT cycles specifically? I want to compute the sign via writing the permutation as a product of cycles so I can apply the formula described above. Since we have already studied combinations, we can also interpret permutations as ‘ordered combinations’. In other words, a permutation is an arrangement of objects in a definite order. for every number I know to which number the permutation sends it. A permutation is a collection or a combination of objects from a set where the order or the arrangement of the chosen objects does matter. Perspective 2: I have a permutation in the form of a black box function, i.e. There are three different types of permutations, including one without repetition and one with repetition. The formula "sign is the product of the signs of the cycles, and a cycle of length $r$ has sign $(-1)^$" is correct whether or not the cycles are disjoint. Eric has taught high school mathematics for more than 20 years and has a masters degree in educational administration. With permutations, the order of the arrangement matters. Perspective 1: I have permutation written as a product of (non-disjoint) cycles, should I recompute it into a product of disjoint cycles in order to more easily compute the sign? The answer can be yes or no depending on your perspective: After some discussion in the comments I think your question is: does decomposing the permutations as a product of DISJOINT cycles have any advantage over decomposing it as ANY product of cycles when you goal is to compute sign.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |