  We consider the structure of roller coaster permutations as introduced by
Ahmed & Snevily[1]. A roller coaster permutation is described as a permuta-
tion that maximizes the total switches from ascending to descending or visa
versa for the permutation and all of its subpermutations simultaneously. This
paper looks at the alternating structure of these permutations and then we
introduce a notion of a condition stronger than alternating for a permutation
that we shall refer to as recursively alternating. We also examine the behav-
ior of what entries can show up in even, odd, and end positions within the
permutations.
