Séminaire Lotharingien de Combinatoire, 85B.49 (2021), 12 pp.
Vassilis-Dionyssis Moustakas
Specializations of Colored Quasisymmetric Functions
Abstract.
We propose a unified approach to prove general formulas for the joint distribution of an Eulerian statistic, a Mahonian statistic and the color sum statistic over a set of colored permutations by specializing Poirier's colored quasisymmetric functions. We apply this method to derive formulas for joint Euler-Mahonian and color sum distributions on colored permutations, derangements and involutions. A number of known formulas are recovered as special cases of our results, including formulas of Biagioli-Zeng, Assaf, Haglund-Loehr-Remmel, Biagioli-Caselli, Faliharimalala-Zeng and Désarménien-Foata. Several new results are also obtained.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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