A pericyclic reaction is a concerted reaction in which the number of rings in the transition state is greater than the total number of rings in the reactant molecules.
mechanism:
# covalent bonds broken = 3
# covalent bonds formed = 3
# covalent bonds broken + # covalent bonds formed = 3 + 3 = 6
# steps = 1
Thus, the reaction is a concerted reaction. The transition state of the reaction can be drawn roughly as follows.
# rings in the reactant molecule = 0
# rings in the transition state = 1
# rings in the transition state > # rings in the reactant molecule
Thus, the reaction is a pericyclic reaction. For more examples of pericyclic reactions, see Cope elimination, Claisen rearrangement, Diels-Alder reaction