论文标题
Eulerian中央限制定理和Carlitz身份在经典Weyl群的正元素中
Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups
论文作者
论文摘要
中央限制定理以对称组$ \ sss_n $中的Eulerian统计统计“下降”（或“剥夺”）而闻名。最近，Fulman，Kim，Lee和Petersen对交替的组$ \ aaa_n $的“下降”给出了中心限制定理，并使用降子在$ \ aaa_n $中提供了Carlitz身份。 在本文中，我们在涉及剥夺的$ \ aaa_n $中给出了中心限制定理。我们将其扩展到B型和D型Coxeter组中的正元素。 Boroweic和Młotkowski列举了$ \ dd_n $的B型下降，DD_N $，D型Coxeter组，并给出了类似的结果。我们为$ \ dd_n $的正面和负部分完善了他们的结果。我们的结果是这些子集对这些子集进行了枚举的结果。
Central Limit Theorems are known for the Eulerian statistic "descent" (or "excedance") in the symmetric group $\SSS_n$. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit Theorem for "descent" over the alternating group $\AAA_n$ and also gave a Carlitz identity in $\AAA_n$ using descents. In this paper, we give a Central Limit Theorem in $\AAA_n$ involving excedances. We extend these to the positive elements in type B and type D Coxeter groups. Boroweic and Młotkowski enumerated type B descents over $\DD_n$, the type D Coxeter group and gave similar results. We refine their results for both the positive and negative part of $\DD_n$. Our results are a consequence of signed enumeration over these subsets.
