Symmetric groupIn abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group defined over a finite set of symbols consists of the permutations that can be performed on the symbols. Since there are ( factorial) such permutation operations, the order (number of elements) of the symmetric group is .
CaffeineCaffeine is a central nervous system (CNS) stimulant of the methylxanthine class. It is mainly used recreationally, as a eugeroic (wakefulness promoter) or as a mild cognitive enhancer to increase alertness and attentional performance. Caffeine acts by blocking binding of adenosine to the adenosine A1 receptor, which enhances release of the neurotransmitter acetylcholine. Caffeine has a three-dimensional structure similar to that of adenosine, which allows it to bind and block its receptors.
Representation theory of the symmetric groupIn mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained. This has a large area of potential applications, from symmetric function theory to quantum chemistry studies of atoms, molecules and solids. The symmetric group Sn has order n!. Its conjugacy classes are labeled by partitions of n.
