In mathematics, the term cycle decomposition can mean:
- In graph theory, a cycle decomposition is a partitioning of the vertices of a graph into subsets, such that the vertices in each subset lie on a cycle.
- In group theory, a cycle decomposition is a useful convention for expressing a permutation in terms of its constituent cycles.
In commutative algebra and linear algebra, cyclic decomposition refers to writing a finitely generated module over a principal ideal domain as the direct sum of cyclic modules and one free module.
Famous quotes containing the word cycle:
“The cycle of the machine is now coming to an end. Man has learned much in the hard discipline and the shrewd, unflinching grasp of practical possibilities that the machine has provided in the last three centuries: but we can no more continue to live in the world of the machine than we could live successfully on the barren surface of the moon.”
—Lewis Mumford (1895–1990)