An Eades-McKay Algorithm for Well-Formed Parentheses Strings

Let T(n) be the set of all well-formed parentheses strings of length 2n. We show that the elements of T(n) can be listed so that successive strings diier by the transposition of a left and a right parenthesis. Furthermore, between the two parentheses that are transposed, only left parentheses occur. Our listing is a modiication of the well-known Eades-McKay 4] algorithm for generating combinations. Like that algorithm, ours generates strings from the lexico-graphically greatest string to the lexicographically least and can be implemented so that each string is generated in constant time, in an amortized sense.