Abstract: We study the equivalence classes of words generated by
the weak associative law To this aim, we use a bijection
between words and binary trees. This leads to consider a restricted rotation.
Nontrivial equivalence classes of words with n open and n close
parentheses are enumerated by the sequence where is the nth
Fibonacci number. The rotation ordering induces a lattice structure on these
equivalence classes.
Keywords and phrases: weak associativity, binary trees, rotation.
