  We consider the problem of upper bounding the number of circular
transpositions needed to sort a permutation. It is well known that any
permutation can be sorted using at most $n(n-1)/2$ adjacent transpositions. We
show that, if we allow all adjacent transpositions, as well as the
transposition that interchanges the element in position 1 with the element in
the last position, then the number of transpositions needed is at most $n^2/4$.
This answers an open question posed by Feng, Chitturi and Sudborough (2010).

Discrete Mathematics;Combinatorics