着色拟对称函数的特殊化与 Euler–Mahonian 恒等式
Specializations of colored quasisymmetric functions and Euler-Mahonian identities
AI总结：
本文通过特殊化 Poirier 着色拟对称函数，建立统一框架推导着色置换上 Euler–Mahonian 联合分布公式，统一并推广多个已知结果，且在有符号置换上引入新的双参数 flag major index 并给出分布公式。
摘要：
我们提出一种统一方法，通过对 Poirier 的着色拟对称函数进行特殊化，证明一组着色置换上 Euler 统计量与 Mahonian 统计量联合分布的一般公式。我们将此方法应用于推导着色置换、错位置换和对合上的 Euler–Mahonian 分布公式。许多已知公式作为我们结果的特例被重新得到，包括 Biagioli–Zeng、Assaf、Haglund–Loehr–Remmel、Chow–Mansour、Biagioli–Caselli、Bagno–Biagioli、Faliharimalala–Zeng 的公式。同时还获得了若干新结果。例如，在有符号置换上引入了一个双参数 flag major index，并证明了其分布以及它与若干 Euler 型伴随统计量联合分布的公式。
英文摘要：
We propose a unified approach to prove general formulas for the joint distribution of an Eulerian and a Mahonian statistic over a set of colored permutations by specializing Poirier's colored quasisymmetric functions. We apply this method to derive formulas for Euler-Mahonian 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, Chow-Mansour, Biagioli-Caselli, Bagno-Biagioli, Faliharimalala-Zeng. Several new results are also obtained. For instance, a two-parameter flag major index on signed permutations is introduced and formulas for its distribution and its joint distribution with some Eulerian partners are proven.
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