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We propose a unified approach to prove general formulas for the jointdistribution of an Eulerian and a Mahonian statistic over a set of coloredpermutations by specializing Poirier's colored quasisymmetric functions. Weapply this method to derive formulas for Euler-Mahonian distributions oncolored permutations, derangements and involutions. A number of known formulasare recovered as special cases of our results, including formulas ofBiagioli-Zeng, Assaf, Haglund-Loehr-Remmel, Chow-Mansour, Biagioli-Caselli,Bagno-Biagioli, Faliharimalala-Zeng. Several new results are also obtained. Forinstance, a two-parameter flag major index on signed permutations is introducedand formulas for its distribution and its joint distribution with some Eulerianpartners are proven.

Specializations of colored quasisymmetric functions and Euler-Mahonian identities