Rearrangement

Rearrangement is the process of changing the order or arrangement of components within a system, resulting in a new configuration. The term is used across disciplines to describe changes in connectivity or sequence that preserve the same components, at least in part.

In chemistry, rearrangements refer to reactions in which bonds or substituents shift within a molecule to form a different structure without adding or removing atoms overall. Common classes include sigmatropic rearrangements, such as the Claisen and Cope rearrangements, and carbocation rearrangements like hydride and alkyl shifts that relocate positive charges and substituents.

In genetics and genomics, chromosomal rearrangements involve changes in the arrangement of genetic material, including translocations, inversions, duplications, and deletions. These can occur through errors in DNA replication or repair and may be benign, contribute to disease, or drive evolutionary changes.

In mathematics, rearrangement concerns permuting the order of terms in sequences or series. The Riemann rearrangement theorem shows that a conditionally convergent series can be rearranged to converge to any value or to diverge. Rearrangement concepts also appear in linguistics, music, and data organization, where the order of elements affects structure and interpretation.