The master's thesis develops the theory of the algebra of colored quasisymmetric functions and explores its close connection with colored permutations and colored partially ordered sets. A generating function can be assigned to the latter within the realm of colored quasisymmetric functions, so that the properties of the partial orders naturally transfer to the properties of their generating functions. The theory is then applied to two colored extensions of classical theorems. These are the decomposition of Schur functions and the Stanley's shuffling theorem. The content is linked to related results from enumerative combinatorics. Among other things, we indicate how to obtain expressions for the distributions of colored permutations through specializations of colored quasisymmetric functions.
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