标题： 关于双陪集和自逆双陪集的枚举 显示英文标题

标题： On the enumeration of double cosets and self-inverse double cosets

摘要： 双陪集在组合学的许多上下文中出现，例如在通过对称性枚举某些对象时。 形式为 $H\backslash G / H$ 的商中的双陪集有一个逆，并且可以是自己的逆。 本文提出了各种枚举双陪集的公式，特别是自逆双陪集的公式。 我们研究了经典群中的双陪集，尤其是对称群和一般线性群，解释了如何获取应用这些公式的共轭类信息。 我们还考虑了 B 型 Coxeter 群的抛物子群的双陪集。 显示英文摘要

摘要： Double cosets appear in many contexts in combinatorics, for example in the enumeration of certain objects up to symmetries. Double cosets in a quotient of the form $H\backslash G / H$ have an inverse, and can be their own inverse. In this paper we present various formulas enumerating double cosets, and in particular self-inverse double cosets. We study double cosets in classical groups, especially the symmetric groups and the general linear groups, explaining how to obtain the informations on their conjugacy classes required to apply our formulas. We also consider double cosets of parabolic subgroups of Coxeter groups of type B.