  A Gauss paragraph is a combinatorial formulation of a generic closed curve
with multiple components on some surface. A virtual string is a collection of
circles with arrows that represent the crossings of such a curve. Every closed
curve has an underlying virtual string and every virtual string has an
underlying Gauss paragraph. A word-wise partition is a partition of the
alphabet set of a Gauss paragraph that satisfies certain conditions with
respect to the Gauss paragraph. In this paper we use the theory of virtual
strings to obtain a combinatorial description of closed curves in the 2-sphere
(and therefore 2-dimensional Euclidean space) in terms of Gauss paragraphs and
word-wise partitions.
