论文标题
彩色的准对称功能和欧拉·马霍尼亚身份的专业
Specializations of colored quasisymmetric functions and Euler-Mahonian identities
论文作者
论文摘要
我们提出了一种统一的方法，以证明欧拉（Eulerian）和玛霍尼（Mahonian）统计量在一组有色置换术的联合分布中，通过专门利用Poirier的有色准对称函数来证明一般公式。我们将此方法应用于在有色置换，毁灭和互动上为欧拉 - 玛霍尼分布的公式。许多已知的公式被回收为我们结果的特殊情况，包括Biagioli-Zeng，Assaf，Haglund-Loehr-Remmel，Chow-Mansour，Biagioli-Caselli，Bagno-Biagioli，faliharimalalala-Zeng的公式。还获得了几个新结果。例如，引入了签名排列的两参数标志主要指数，并证明了其分布和与某些欧拉合作伙伴的联合分配的公式。
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.
