  The free $\mathbb{Z}$-module generated from the set of non-trivial homotopy
classes of closed curves on an oriented surface has the structure of Lie
bialgebra by two operations, the Goldman bracket and Turaev cobracket. M. Chas
gave a combinatorial redefinition of these two operations through a natural
identification of the homotopy classes of closed curves on the surface with the
cyclic words in the generators and their inverses of the fundamental group of
the surface. We present a new approach to give a combinatorial definition of
the bracket and cobracket, focusing on the information given by the partitions
of cyclic words.
