Reciprocity and rationality for the greedy normal form of a Coxeter group

Poincaré series of double coset representatives of Coxeter groups

Let $(W,S)$ be a Coxeter system of finite rank and let $J,K\subset S$. We study the rationality of the Poincaré series of the set of representatives of minimal length of $(W_J,W_K)$-double cosets of $W$: we conclude that it depends mostly on the rationality of the Poincaré series of the normalizers of finite parabolic subgroups of $W$. For affine Weyl groups, we prove that all these series are rational and we give some explicit examples.

自由群中的稳定共轭不变词范数是理性的

The stable conjugation-invariant word norm is rational in free groups

本文证明了自由群及几乎自由Coxeter群上稳定共轭不变词范数的理性性质。

Dyer 群的增长级数

The growth series of Dyer groups

本文在统一框架下研究 Dyer 群关于标准生成集的增长级数，给出了基于标准抛物子群增长级数的递推公式，并据此证明了其有理性及与欧拉特征的密切关系。