论文标题
二面部对簇复合物的筛分
Dihedral Sieving on Cluster Complexes
论文作者
论文摘要
雷纳，斯坦顿和白色的环状筛分现象表征了使用Q-Analogue多项式对有限组集的环状群体作用的稳定剂。欧盟和FU使用Q-Catalan数字显示了每种类型的广义群集复合物上的环状筛分现象。在本文中，我们展示了二面的筛分现象，该现象是由Rao和Suk在每种类型的簇上介绍的。在A型情况下，我们表明Raney数量对N-GON的反射对称k接收和（Q，T）-Fuss-Catalan数字进行了特定评估。我们还为对称群体引入了一种筛分现象，并讨论了二面性筛分的可能性。
The cyclic sieving phenomenon of Reiner, Stanton, and White characterizes the stabilizers of cyclic group actions on finite sets using q-analogue polynomials. Eu and Fu demonstrated a cyclic sieving phenomenon on generalized cluster complexes of every type using the q-Catalan numbers. In this paper, we exhibit the dihedral sieving phenomenon, introduced for odd n by Rao and Suk, on clusters of every type. In the type A case, we show that the Raney numbers count both reflection-symmetric k-angulations of an n-gon and a particular evaluation of the (q,t)-Fuss--Catalan numbers. We also introduce a sieving phenomenon for the symmetric group, and discuss possibilities for dihedral sieving for even n.
