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https://groupprops.subwiki.org/wiki/Cycle_decomposition_for_permutations
A cycle decomposition for is an expression of as a product of disjoint cycles. Here, a cycle is a permutation sending to for and to . Two cycles are disjoint if they do not have any common elements. Any permutation on a finite set has a unique cycle decomposition. In other words, the cycles making up the permutation are uniquely determined.
https://math.stackexchange.com/questions/56029/cycle-decomposition-into-disjoint-cycles
It's a product (with one factor) of disjoint cycles (each cycle in the product is disjoint from any other cycle in the product). The main problem is that you misread the link. It doesn't say every cycle can be decomposed into a product of disjoint cycles, it says every permutation (on a finite set) can be decomposed into a product of disjoint ...
https://math.stackexchange.com/questions/476263/permutations-and-disjoint-cycles
Then take the first number not in that cycle and track its orbit under repeated applications of $\pi$. Keep doing this until all elements of the domain have been exhausted. These orbits never intersect, so you get the decomposition of $\pi$ into a product of pairwise disjoint cycles.
https://www.sciencedirect.com/science/article/pii/0097316572900106
JOURNAL OF COMBINATORIAL THEORY (A) 13, 83-89 (1972) Cycle Decomposition by Disjoint Transpositions M. COHN AND A. LEMPEL Sperry Rand Research Center, Sudbury, Massachusetts 01776 Communicated by W. T. Tutte Received October 7, 1970 We investigate in this paper the cycle structures induced on cyclic permutations by disjoint transpositions or, equivalently, the decomposition …Cited by: 86
http://web.eecs.umich.edu/~valeria/research/thesis/thesis4.pdf
The last decomposition of Example 4.1 is a maximal decomposition. We discuss now some previous work on the subject and introduce some formal denitions re-lated to disjoint support decompositions, before we present our contributions. 4.2 Related work on Disjoint Support Decompositions
https://www.youtube.com/watch?v=vhkovYrx-MU
Apr 22, 2016 · On y voit la décomposition des permutations en produit de cycle de supports disjoint, qui est très utile pour la suite. On applique cette décomposition au calcul de l'ordre d'une permutation.
http://www.mathe2.uni-bayreuth.de/frib/KERBER/h00/node21.html
Notice that, for example, are disjoint cycles. Disjoint cycles and commute, i.e. . (We read compositions of mappings from right to left, so that .) Each permutation of a finite set can be written as a product of pairwise different disjoint cycles, e.g. There are some more examples for …
https://en.wikipedia.org/wiki/Cycle_decomposition_(group_theory)
Cycle notation describes the effect of repeatedly applying the permutation on the elements of the set. It expresses the permutation as a product of cycles; since distinct cycles are disjoint, this is referred to as "decomposition into disjoint cycles".
https://www.sciencedirect.com/science/article/pii/0097316577900413
JOURNAL OF COMBINATORIAL THEORY (A) 23, 198-207 (1977) Cycle Decomposition by Transpositions ISTVAN BECK* Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel, and Department of Mathematics, Universitetet i Bergen, 5014 Bergen, Norway: Communicated by the Managing Editors Received January 14, 1976 We relate the number of cycles …Cited by: 25
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