a special notation is used to describe sigmatropic shifts. each of the carbon atoms on the backbone of the molecule are assigned a position number. sigmatropic rearrangements are described by an order term [i,j]. this means the migration of a σ-bond adjacent to one or more π systems to a new position (i-1) and (j-1) atoms removed from the original location of the σ-bond. when the sum of i and j is an even number, this is an indication of the involvement of a neutral, all c atom chain. an odd number suggests that there is a charged c atom or of a heteroatom lone pair replacing a carbon-carbon double bond. thus, [1,5] and [3,3] shifts become [1,4] and [2,3] shifts with heteroatoms, while preserving symmetry considerations. hydrogens are omitted in the third example for clarity.