perm

Perm is a city in Perm Krai, Russia, located on the Kama River near the western foothills of the Ural Mountains. It serves as the administrative center of Perm Krai and is one of the region’s largest urban centers, with a population of about one million. The city has a diversified economy based on metalworking, machinery, chemicals, and services, and it is a cultural and educational hub, home to several universities and theaters.

The city originated in the 18th century as a center of metal production around ironworks and a growing industrial settlement. It developed into a major industrial and administrative center during the Russian Empire and continued to evolve through the Soviet era and into contemporary Russia.

Perm also refers to the hairstyle known as a permanent wave, used to create curls or waves that last for months. The technique involves chemically breaking and reforming disulfide bonds in hair, typically after wrapping hair around rods, followed by neutralization. The first commercially successful perms were developed in the early 20th century by Karl Nessler and were later refined; modern perms include various methods, such as cold waves and heat-based processes, with varying effects and maintenance requirements.

In mathematics, “perm” is short for permutation, a rearrangement of the elements of a set. Permutations are central to combinatorics and probability, and the factorial function n! gives the number of distinct permutations of a set with n elements. The term is widely used in algorithms, cryptography, and statistical inference.