The Poincaré Series of Coxeter Folding Subgroups
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910209799094272 |
|---|---|
| author | Chalarca, Camilo Augusto Villamil Richmond, Edward |
| author_facet | Chalarca, Camilo Augusto Villamil Richmond, Edward |
| contents | Folding subgroups give a way to realize non-simply-laced Coxeter groups as subgroups of simply-laced Coxeter groups. In this paper, we study how folding subgroups of finite and affine type are distributed length-wise by calculating the length generating function of the subgroup with respect the length of the ambient group. These generating functions have surprisingly nice formulas in terms of $q$-integers and give rise to interesting combinatorial identities on polynomials involving length statistics of both the ambient group and folding subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11057 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Poincaré Series of Coxeter Folding Subgroups Chalarca, Camilo Augusto Villamil Richmond, Edward Combinatorics 20F55, 22E40 Folding subgroups give a way to realize non-simply-laced Coxeter groups as subgroups of simply-laced Coxeter groups. In this paper, we study how folding subgroups of finite and affine type are distributed length-wise by calculating the length generating function of the subgroup with respect the length of the ambient group. These generating functions have surprisingly nice formulas in terms of $q$-integers and give rise to interesting combinatorial identities on polynomials involving length statistics of both the ambient group and folding subgroup. |
| title | The Poincaré Series of Coxeter Folding Subgroups |
| topic | Combinatorics 20F55, 22E40 |
| url | https://arxiv.org/abs/2605.11057 |