A component is any part of a molecule or molecules that function as a unit in a pericyclic reaction.  A component consists of one or more atoms and any of the following types of associated orbitals: 
* An isolated p- or sp-orbital (unfilled or filled, symbol ω) 
* A conjugated π system (symbol π)
* A σ bond (symbol σ)
The electron count of a component is the number of electrons in the orbital(s) of the component:
* The electron count of an unfilled ω orbital (i.e., an empty p orbital) is 0, while that of a filled ω orbital (i.e., a lone pair) is 2.
* The electron count of a conjugated π system with n double bonds is 2n (or 2n + 2, if a (formal) lone pair from a heteroatom or carbanion is conjugated thereto).
* The electron count of a σ bond is 2.
The bond topology of a component can be suprafacial and antarafacial:
* The relationship is suprafacial (symbol: s) when the interactions with the π system or p orbital occur on the same side of the nodal plane (think syn). For a σ bond, it corresponds to interactions occurring on the two "interior" lobes or two "exterior" lobes of the bond.
* The relationship is antarafacial (symbol: a) when the interactions with the π system or p orbital occur on opposite sides of the nodal plane (think anti). For a σ bond, it corresponds to interactions occurring on one "interior" lobe and one "exterior" lobe of the bond.
Using this notation, all pericyclic reactions can be assigned a descriptor, consisting of a series of symbols N, connected by + signs and enclosed in brackets, describing, in order, the type of orbital(s), number of electrons, and bond topology involved for each component.  Some illustrative examples follow:
* The Diels-Alder reaction (a (4+2)-cycloaddition) is [4 + 2].
* The 1,3-dipolar cycloaddition of ozone and an olefin in the first step of ozonolysis (a (3+2)-cycloaddition) is [4 + 2]. 
* The cheletropic addition of sulfur dioxide to 1,3-butadiene (a (4+1)-cheletropic addition) is [0 + 4] + [2 + 4].
* The Cope rearrangement (a [3,3]-sigmatropic shift) is [2 + 2 + 2] or [2 + 2 + 2].
* The [1,3]-alkyl migration with inversion at carbon discovered by Berson (a [1,3]-sigmatropic shift) is [2 + 2].
* The conrotatory electrocyclic ring closing of 1,3-butadiene (a 4π-electrocyclization) is [4].
* The conrotatory electrocyclic ring opening of cyclobutene (a reverse 4π-electrocyclization) is [2 + 2] or [2 + 2].
* The disrotatory electrocyclic ring closing of 1,3-cyclooctadien-5-ide anion (a 6π-electrocyclization) is [6].
* A Wagner-Meerwein shift of a carbocation (a [1,2]-sigmatropic shift) is [0 + 2].
Antarafacial and suprafacial are associated with (conrotation or inversion) and (disrotation or retention), respectively. A single descriptor may correspond to two pericyclic processes that are chemically distinct, that a reaction and its microscopic reverse are often described with two different descriptors, and that a single process may have more than a one correct descriptor.  One can verify, using the pericyclic selection rule given below, that all of these reactions are allowed processes.